LMFDB - Embedded newform 87.2.g.b.25.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(7,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.3
Root			$2.41546 + 1.16323i$ of defining polynomial
Character	$\chi$	$=$	87.25
Dual form			87.2.g.b.7.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.596570 - 2.61374i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-4.67383 - 2.25080i) q^{4} +(-0.692177 + 3.03263i) q^{5} +(-0.596570 - 2.61374i) q^{6} +(2.13550 - 1.02840i) q^{7} +(-5.32817 + 6.68131i) q^{8} +(0.623490 - 0.781831i) q^{9} +(7.51358 + 3.61835i) q^{10} +(1.62277 + 2.03489i) q^{11} -5.18756 q^{12} +(-1.43935 - 1.80488i) q^{13} +(-1.41401 - 6.19518i) q^{14} +(0.692177 + 3.03263i) q^{15} +(7.81583 + 9.80074i) q^{16} -4.83107 q^{17} +(-1.67155 - 2.09606i) q^{18} +(-1.47595 - 0.710781i) q^{19} +(10.0609 - 12.6160i) q^{20} +(1.47782 - 1.85312i) q^{21} +(6.28677 - 3.02755i) q^{22} +(0.263303 + 1.15361i) q^{23} +(-1.90160 + 8.33146i) q^{24} +(-4.21288 - 2.02881i) q^{25} +(-5.57617 + 2.68534i) q^{26} +(0.222521 - 0.974928i) q^{27} -12.2957 q^{28} +(5.05191 + 1.86501i) q^{29} +8.33945 q^{30} +(-1.28688 + 5.63821i) q^{31} +(14.8805 - 7.16606i) q^{32} +(2.34497 + 1.12928i) q^{33} +(-2.88207 + 12.6272i) q^{34} +(1.64062 + 7.18803i) q^{35} +(-4.67383 + 2.25080i) q^{36} +(4.30094 - 5.39321i) q^{37} +(-2.73831 + 3.43373i) q^{38} +(-2.07992 - 1.00163i) q^{39} +(-16.5739 - 20.7830i) q^{40} -7.66791 q^{41} +(-3.96197 - 4.96815i) q^{42} +(-0.419989 - 1.84009i) q^{43} +(-3.00442 - 13.1632i) q^{44} +(1.93944 + 2.43198i) q^{45} +3.17231 q^{46} +(-5.79950 - 7.27234i) q^{47} +(11.2942 + 5.43900i) q^{48} +(-0.861665 + 1.08049i) q^{49} +(-7.81608 + 9.80105i) q^{50} +(-4.35265 + 2.09612i) q^{51} +(2.66483 + 11.6754i) q^{52} +(1.15113 - 5.04343i) q^{53} +(-2.41546 - 1.16323i) q^{54} +(-7.29430 + 3.51275i) q^{55} +(-4.50723 + 19.7475i) q^{56} -1.63818 q^{57} +(7.88847 - 12.0918i) q^{58} -4.90494 q^{59} +(3.59071 - 15.7319i) q^{60} +(10.3934 - 5.00522i) q^{61} +(13.9691 + 6.72717i) q^{62} +(0.527426 - 2.31080i) q^{63} +(-4.27413 - 18.7262i) q^{64} +(6.46982 - 3.11570i) q^{65} +(4.35058 - 5.45546i) q^{66} +(-4.34830 + 5.45260i) q^{67} +(22.5796 + 10.8738i) q^{68} +(0.737759 + 0.925121i) q^{69} +19.7664 q^{70} +(2.32918 + 2.92070i) q^{71} +(1.90160 + 8.33146i) q^{72} +(-0.532592 - 2.33344i) q^{73} +(-11.5306 - 14.4590i) q^{74} -4.67594 q^{75} +(5.29852 + 6.64413i) q^{76} +(5.55812 + 2.67665i) q^{77} +(-3.85883 + 4.83882i) q^{78} +(2.34395 - 2.93923i) q^{79} +(-35.1319 + 16.9187i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-4.57445 + 20.0420i) q^{82} +(9.54570 + 4.59697i) q^{83} +(-11.0780 + 5.33491i) q^{84} +(3.34396 - 14.6508i) q^{85} -5.06009 q^{86} +(5.36081 - 0.511626i) q^{87} -22.2421 q^{88} +(1.26895 - 5.55963i) q^{89} +(7.51358 - 3.61835i) q^{90} +(-4.92988 - 2.37411i) q^{91} +(1.36590 - 5.98440i) q^{92} +(1.28688 + 5.63821i) q^{93} +(-22.4678 + 10.8199i) q^{94} +(3.17715 - 3.98402i) q^{95} +(10.2976 - 12.9128i) q^{96} +(-15.1300 - 7.28624i) q^{97} +(2.31009 + 2.89676i) q^{98} +2.60272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.596570	−	2.61374i	0.421839	−	1.84820i	−0.0997685	−	0.995011i	$-0.531810\pi$
$2$	0.596570	−	2.61374i	0.421839	−	1.84820i	0.521607	−	0.853186i	$-0.325333\pi$
$3$	0.900969	−	0.433884i	0.520175	−	0.250503i
$3$	0.900969	−	0.433884i	0.520175	−	0.250503i
$4$	−4.67383	−	2.25080i	−2.33691	−	1.12540i
$5$	−0.692177	+	3.03263i	−0.309551	+	1.35623i	0.545684	+	0.837991i	$0.316270\pi$
$5$	−0.692177	+	3.03263i	−0.309551	+	1.35623i	−0.855235	+	0.518241i	$0.826587\pi$
$6$	−0.596570	−	2.61374i	−0.243549	−	1.06706i
$7$	2.13550	−	1.02840i	0.807145	−	0.388701i	0.0156510	−	0.999878i	$-0.495018\pi$
$7$	2.13550	−	1.02840i	0.807145	−	0.388701i	0.791494	+	0.611177i	$0.209304\pi$
$8$	−5.32817	+	6.68131i	−1.88379	+	2.36220i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	7.51358	+	3.61835i	2.37600	+	1.14422i
$11$	1.62277	+	2.03489i	0.489283	+	0.613542i	0.963774	−	0.266719i	$-0.0859394\pi$
$11$	1.62277	+	2.03489i	0.489283	+	0.613542i	−0.474491	+	0.880260i	$0.657368\pi$
$12$	−5.18756			−1.49752
$13$	−1.43935	−	1.80488i	−0.399203	−	0.500584i	0.541084	−	0.840969i	$-0.318014\pi$
$13$	−1.43935	−	1.80488i	−0.399203	−	0.500584i	−0.940286	+	0.340384i	$0.889443\pi$
$14$	−1.41401	−	6.19518i	−0.377910	−	1.65573i
$15$	0.692177	+	3.03263i	0.178719	+	0.783021i
$16$	7.81583	+	9.80074i	1.95396	+	2.45019i
$17$	−4.83107			−1.17171			−0.585854	−	0.810417i	$-0.699241\pi$
$17$	−4.83107			−1.17171			−0.585854	+	0.810417i	$0.699241\pi$
$18$	−1.67155	−	2.09606i	−0.393989	−	0.494046i
$19$	−1.47595	−	0.710781i	−0.338606	−	0.163064i	0.256851	−	0.966451i	$-0.417315\pi$
$19$	−1.47595	−	0.710781i	−0.338606	−	0.163064i	−0.595458	+	0.803387i	$0.703029\pi$
$20$	10.0609	−	12.6160i	2.24970	−	2.82103i
$21$	1.47782	−	1.85312i	0.322486	−	0.404384i
$22$	6.28677	−	3.02755i	1.34034	−	0.645476i
$23$	0.263303	+	1.15361i	0.0549025	+	0.240544i	0.994932	−	0.100549i	$-0.0320600\pi$
$23$	0.263303	+	1.15361i	0.0549025	+	0.240544i	−0.940030	+	0.341093i	$0.889203\pi$
$24$	−1.90160	+	8.33146i	−0.388163	+	1.70065i
$25$	−4.21288	−	2.02881i	−0.842575	−	0.405763i
$26$	−5.57617	+	2.68534i	−1.09358	+	0.526639i
$27$	0.222521	−	0.974928i	0.0428242	−	0.187625i
$28$	−12.2957			−2.32367
$29$	5.05191	+	1.86501i	0.938115	+	0.346323i
$29$	5.05191	+	1.86501i	0.938115	+	0.346323i
$30$	8.33945			1.52257
$31$	−1.28688	+	5.63821i	−0.231131	+	1.01265i	0.717572	+	0.696484i	$0.245253\pi$
$31$	−1.28688	+	5.63821i	−0.231131	+	1.01265i	−0.948703	+	0.316168i	$0.897604\pi$
$32$	14.8805	−	7.16606i	2.63052	−	1.26679i
$33$	2.34497	+	1.12928i	0.408207	+	0.196582i
$34$	−2.88207	+	12.6272i	−0.494272	+	2.16555i
$35$	1.64062	+	7.18803i	0.277316	+	1.21500i
$36$	−4.67383	+	2.25080i	−0.778971	+	0.375133i
$37$	4.30094	−	5.39321i	0.707070	−	0.886637i	−0.290460	−	0.956887i	$-0.593808\pi$
$37$	4.30094	−	5.39321i	0.707070	−	0.886637i	0.997529	+	0.0702498i	$0.0223796\pi$
$38$	−2.73831	+	3.43373i	−0.444212	+	0.557024i
$39$	−2.07992	−	1.00163i	−0.333053	−	0.160390i
$40$	−16.5739	−	20.7830i	−2.62056	−	3.28608i
$41$	−7.66791			−1.19753			−0.598763	−	0.800926i	$-0.704341\pi$
$41$	−7.66791			−1.19753			−0.598763	+	0.800926i	$0.704341\pi$
$42$	−3.96197	−	4.96815i	−0.611345	−	0.766602i
$43$	−0.419989	−	1.84009i	−0.0640478	−	0.280612i	0.932755	−	0.360510i	$-0.117397\pi$
$43$	−0.419989	−	1.84009i	−0.0640478	−	0.280612i	−0.996803	+	0.0798987i	$0.974540\pi$
$44$	−3.00442	−	13.1632i	−0.452934	−	1.98443i
$45$	1.93944	+	2.43198i	0.289114	+	0.362538i
$46$	3.17231			0.467732
$47$	−5.79950	−	7.27234i	−0.845944	−	1.06078i	−0.997382	−	0.0723132i	$-0.976962\pi$
$47$	−5.79950	−	7.27234i	−0.845944	−	1.06078i	0.151438	−	0.988467i	$-0.451610\pi$
$48$	11.2942	+	5.43900i	1.63018	+	0.785052i
$49$	−0.861665	+	1.08049i	−0.123095	+	0.154356i
$50$	−7.81608	+	9.80105i	−1.10536	+	1.38608i
$51$	−4.35265	+	2.09612i	−0.609493	+	0.293516i
$52$	2.66483	+	11.6754i	0.369545	+	1.61908i
$53$	1.15113	−	5.04343i	0.158120	−	0.692768i	−0.832259	−	0.554387i	$-0.812953\pi$
$53$	1.15113	−	5.04343i	0.158120	−	0.692768i	0.990379	−	0.138381i	$-0.0441899\pi$
$54$	−2.41546	−	1.16323i	−0.328703	−	0.158295i
$55$	−7.29430	+	3.51275i	−0.983563	+	0.473659i
$56$	−4.50723	+	19.7475i	−0.602304	+	2.63887i
$57$	−1.63818			−0.216983
$58$	7.88847	−	12.0918i	1.03581	−	1.58773i
$59$	−4.90494			−0.638569			−0.319285	−	0.947659i	$-0.603443\pi$
$59$	−4.90494			−0.638569			−0.319285	+	0.947659i	$0.603443\pi$
$60$	3.59071	−	15.7319i	0.463559	−	2.03098i
$61$	10.3934	−	5.00522i	1.33074	−	0.640852i	0.372828	−	0.927901i	$-0.378388\pi$
$61$	10.3934	−	5.00522i	1.33074	−	0.640852i	0.957916	+	0.287048i	$0.0926740\pi$
$62$	13.9691	+	6.72717i	1.77408	+	0.854352i
$63$	0.527426	−	2.31080i	0.0664494	−	0.291134i
$64$	−4.27413	−	18.7262i	−0.534266	−	2.34077i
$65$	6.46982	−	3.11570i	0.802482	−	0.386455i
$66$	4.35058	−	5.45546i	0.535519	−	0.671520i
$67$	−4.34830	+	5.45260i	−0.531229	+	0.666141i	−0.972951	−	0.231012i	$-0.925796\pi$
$67$	−4.34830	+	5.45260i	−0.531229	+	0.666141i	0.441722	+	0.897152i	$0.354368\pi$
$68$	22.5796	+	10.8738i	2.73818	+	1.31864i
$69$	0.737759	+	0.925121i	0.0888158	+	0.111371i
$70$	19.7664			2.36254
$71$	2.32918	+	2.92070i	0.276423	+	0.346623i	0.900592	−	0.434666i	$-0.143134\pi$
$71$	2.32918	+	2.92070i	0.276423	+	0.346623i	−0.624169	+	0.781289i	$0.714562\pi$
$72$	1.90160	+	8.33146i	0.224106	+	0.981871i
$73$	−0.532592	−	2.33344i	−0.0623351	−	0.273108i	0.934150	−	0.356881i	$-0.116160\pi$
$73$	−0.532592	−	2.33344i	−0.0623351	−	0.273108i	−0.996485	+	0.0837733i	$0.973303\pi$
$74$	−11.5306	−	14.4590i	−1.34041	−	1.68082i
$75$	−4.67594			−0.539931
$76$	5.29852	+	6.64413i	0.607782	+	0.762134i
$77$	5.55812	+	2.67665i	0.633406	+	0.305032i
$78$	−3.85883	+	4.83882i	−0.436927	+	0.547889i
$79$	2.34395	−	2.93923i	0.263716	−	0.330689i	−0.632290	−	0.774732i	$-0.717885\pi$
$79$	2.34395	−	2.93923i	0.263716	−	0.330689i	0.896005	+	0.444043i	$0.146456\pi$
$80$	−35.1319	+	16.9187i	−3.92787	+	1.89156i
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−4.57445	+	20.0420i	−0.505163	+	2.21326i
$83$	9.54570	+	4.59697i	1.04778	+	0.504583i	0.876882	−	0.480707i	$-0.159620\pi$
$83$	9.54570	+	4.59697i	1.04778	+	0.504583i	0.170895	+	0.985289i	$0.445334\pi$
$84$	−11.0780	+	5.33491i	−1.20871	+	0.582086i
$85$	3.34396	−	14.6508i	0.362703	−	1.58911i
$86$	−5.06009			−0.545643
$87$	5.36081	−	0.511626i	0.574739	−	0.0548521i
$88$	−22.2421			−2.37101
$89$	1.26895	−	5.55963i	0.134508	−	0.589320i	−0.862079	−	0.506774i	$-0.830838\pi$
$89$	1.26895	−	5.55963i	0.134508	−	0.589320i	0.996587	−	0.0825457i	$-0.0263050\pi$
$90$	7.51358	−	3.61835i	0.792001	−	0.381408i
$91$	−4.92988	−	2.37411i	−0.516792	−	0.248874i
$92$	1.36590	−	5.98440i	0.142405	−	0.623917i
$93$	1.28688	+	5.63821i	0.133444	+	0.584655i
$94$	−22.4678	+	10.8199i	−2.31738	+	1.11599i
$95$	3.17715	−	3.98402i	0.325969	−	0.408752i
$96$	10.2976	−	12.9128i	1.05100	−	1.31791i
$97$	−15.1300	−	7.28624i	−1.53622	−	0.739806i	−0.541337	−	0.840806i	$-0.682082\pi$
$97$	−15.1300	−	7.28624i	−1.53622	−	0.739806i	−0.994886	+	0.101000i	$0.967796\pi$
$98$	2.31009	+	2.89676i	0.233354	+	0.292617i
$99$	2.60272			0.261583
$100$	15.1238	+	18.9646i	1.51238	+	1.89646i
$101$	−1.01964	−	4.46734i	−0.101458	−	0.444517i	−0.999984	−	0.00559720i	$-0.998218\pi$
$101$	−1.01964	−	4.46734i	−0.101458	−	0.444517i	0.898526	−	0.438920i	$-0.144639\pi$
$102$	2.88207	+	12.6272i	0.285368	+	1.25028i
$103$	6.56608	+	8.23361i	0.646975	+	0.811281i	0.991856	−	0.127365i	$-0.0406521\pi$
$103$	6.56608	+	8.23361i	0.646975	+	0.811281i	−0.344881	+	0.938647i	$0.612081\pi$
$104$	19.7281			1.93449
$105$	4.59692	+	5.76435i	0.448613	+	0.562543i
$106$	−12.4955	−	6.01751i	−1.21367	−	0.584473i
$107$	8.57509	−	10.7528i	0.828985	−	1.03951i	−0.169556	−	0.985520i	$-0.554233\pi$
$107$	8.57509	−	10.7528i	0.828985	−	1.03951i	0.998541	−	0.0539937i	$-0.0171951\pi$
$108$	−3.23439	+	4.05579i	−0.311229	+	0.390269i
$109$	4.82225	−	2.32227i	0.461888	−	0.222434i	−0.188444	−	0.982084i	$-0.560344\pi$
$109$	4.82225	−	2.32227i	0.461888	−	0.222434i	0.650332	+	0.759650i	$0.274630\pi$
$110$	4.82987	+	21.1610i	0.460510	+	2.01763i
$111$	1.53499	−	6.72522i	0.145695	−	0.638329i
$112$	26.7699	+	12.8917i	2.52952	+	1.21815i
$113$	9.72860	−	4.68504i	0.915189	−	0.440732i	0.0838381	−	0.996479i	$-0.473282\pi$
$113$	9.72860	−	4.68504i	0.915189	−	0.440732i	0.831351	+	0.555747i	$0.187568\pi$
$114$	−0.977290	+	4.28179i	−0.0915316	+	0.401026i
$115$	−3.68071			−0.343228
$116$	−19.4140	−	20.0875i	−1.80254	−	1.86508i
$117$	−2.30853			−0.213424
$118$	−2.92614	+	12.8203i	−0.269373	+	1.18020i
$119$	−10.3168	+	4.96830i	−0.945738	+	0.455443i
$120$	−23.9500	−	11.5337i	−2.18632	−	1.05288i
$121$	0.940341	−	4.11990i	0.0854856	−	0.374537i
$122$	−6.88194	−	30.1518i	−0.623062	−	2.72981i
$123$	−6.90855	+	3.32698i	−0.622923	+	0.299984i
$124$	18.7051	−	23.4555i	1.67977	−	2.10637i
$125$	−0.628496	+	0.788109i	−0.0562144	+	0.0704906i
$126$	−5.72521	−	2.75711i	−0.510042	−	0.245623i
$127$	10.5127	+	13.1825i	0.932851	+	1.16976i	0.985248	+	0.171132i	$0.0547423\pi$
$127$	10.5127	+	13.1825i	0.932851	+	1.16976i	−0.0523973	+	0.998626i	$0.516686\pi$
$128$	−18.4631			−1.63192
$129$	−1.17678	−	1.47564i	−0.103610	−	0.129923i
$130$	−4.28394	−	18.7692i	−0.375727	−	1.64617i
$131$	−1.01316	−	4.43896i	−0.0885206	−	0.387834i	0.911188	−	0.411992i	$-0.135167\pi$
$131$	−1.01316	−	4.43896i	−0.0885206	−	0.387834i	−0.999708	+	0.0241577i	$0.992310\pi$
$132$	−8.41820	−	10.5561i	−0.732710	−	0.918790i
$133$	−3.88287			−0.336688
$134$	11.6576	+	14.6182i	1.00707	+	1.26282i
$135$	2.80257	+	1.34965i	0.241207	+	0.116159i
$136$	25.7408	−	32.2779i	2.20725	−	2.76781i
$137$	−13.7225	+	17.2075i	−1.17239	+	1.47014i	−0.319861	+	0.947465i	$0.603636\pi$
$137$	−13.7225	+	17.2075i	−1.17239	+	1.47014i	−0.852534	+	0.522672i	$0.824935\pi$
$138$	2.85816	−	1.37642i	0.243302	−	0.117168i
$139$	1.80101	+	7.89075i	0.152760	+	0.669284i	0.992076	+	0.125641i	$0.0400986\pi$
$139$	1.80101	+	7.89075i	0.152760	+	0.669284i	−0.839316	+	0.543644i	$0.817044\pi$
$140$	8.51081	−	37.2883i	0.719295	−	3.15144i
$141$	−8.38052	−	4.03584i	−0.705767	−	0.339879i
$142$	9.02347	−	4.34548i	0.757233	−	0.364664i
$143$	1.33701	−	5.85781i	0.111806	−	0.489855i
$144$	12.5356			1.04464
$145$	−9.15269	+	14.0296i	−0.760089	+	1.16510i
$146$	−6.41673			−0.531053
$147$	−0.307525	+	1.34735i	−0.0253642	+	0.111128i
$148$	−32.2408	+	15.5264i	−2.65018	+	1.27626i
$149$	−0.670037	−	0.322673i	−0.0548916	−	0.0264344i	0.406237	−	0.913768i	$-0.366841\pi$
$149$	−0.670037	−	0.322673i	−0.0548916	−	0.0264344i	−0.461128	+	0.887334i	$0.652555\pi$
$150$	−2.78953	+	12.2217i	−0.227764	+	0.997898i
$151$	3.84695	+	16.8546i	0.313060	+	1.37161i	0.849465	+	0.527646i	$0.176925\pi$
$151$	3.84695	+	16.8546i	0.313060	+	1.37161i	−0.536404	+	0.843961i	$0.680218\pi$
$152$	12.6131	−	6.07413i	1.02305	−	0.492677i
$153$	−3.01213	+	3.77709i	−0.243516	+	0.305359i
$154$	10.3119	−	12.9307i	0.830955	−	1.04198i
$155$	−16.2078	−	7.80528i	−1.30184	−	0.626935i
$156$	7.46669	+	9.36293i	0.597813	+	0.749634i
$157$	−0.399286			−0.0318665			−0.0159332	−	0.999873i	$-0.505072\pi$
$157$	−0.399286			−0.0318665			−0.0159332	+	0.999873i	$0.505072\pi$
$158$	−6.28405	−	7.87995i	−0.499932	−	0.626895i
$159$	−1.15113	−	5.04343i	−0.0912905	−	0.399970i
$160$	11.4321	+	50.0872i	0.903784	+	3.95974i
$161$	1.74866	+	2.19275i	0.137814	+	0.172813i
$162$	−2.68096			−0.210636
$163$	6.18092	+	7.75063i	0.484127	+	0.607076i	0.962567	−	0.271044i	$-0.0873690\pi$
$163$	6.18092	+	7.75063i	0.484127	+	0.607076i	−0.478440	+	0.878120i	$0.658798\pi$
$164$	35.8385	+	17.2589i	2.79852	+	1.34769i
$165$	−5.04781	+	6.32976i	−0.392972	+	0.492771i
$166$	17.7100	−	22.2076i	1.37456	−	1.72364i
$167$	10.5584	−	5.08467i	0.817036	−	0.393464i	0.0217990	−	0.999762i	$-0.493061\pi$
$167$	10.5584	−	5.08467i	0.817036	−	0.393464i	0.795237	+	0.606298i	$0.207346\pi$
$168$	4.50723	+	19.7475i	0.347741	+	1.52355i
$169$	1.70689	−	7.47836i	0.131299	−	0.575259i
$170$	−36.2987	−	17.4805i	−2.78398	−	1.34069i
$171$	−1.47595	+	0.710781i	−0.112869	+	0.0543547i
$172$	−2.17872	+	9.54559i	−0.166126	+	0.727844i
$173$	8.14339			0.619131			0.309565	−	0.950878i	$-0.399816\pi$
$173$	8.14339			0.619131			0.309565	+	0.950878i	$0.399816\pi$
$174$	1.86084	−	14.3170i	0.141070	−	1.08537i
$175$	−11.0831			−0.837800
$176$	−7.26012	+	31.8087i	−0.547252	+	2.39767i
$177$	−4.41920	+	2.12818i	−0.332168	+	0.159963i
$178$	−13.7744	−	6.63342i	−1.03244	−	0.497196i
$179$	−2.39845	+	10.5083i	−0.179268	+	0.785426i	0.802700	+	0.596383i	$0.203396\pi$
$179$	−2.39845	+	10.5083i	−0.179268	+	0.785426i	−0.981969	+	0.189044i	$0.939461\pi$
$180$	−3.59071	−	15.7319i	−0.267636	−	1.17259i
$181$	−18.5712	+	8.94342i	−1.38039	+	0.664759i	−0.969082	−	0.246738i	$-0.920641\pi$
$181$	−18.5712	+	8.94342i	−1.38039	+	0.664759i	−0.411305	+	0.911498i	$0.634927\pi$
$182$	−9.14632	+	11.4691i	−0.677971	+	0.850148i
$183$	7.19248	−	9.01909i	0.531684	−	0.666710i
$184$	−9.11053	−	4.38740i	−0.671637	−	0.323443i
$185$	13.3786	+	16.7762i	0.983612	+	1.23341i
$186$	15.5046			1.13685
$187$	−7.83972	−	9.83069i	−0.573297	−	0.718891i
$188$	10.7373	+	47.0431i	0.783097	+	3.43097i
$189$	−0.527426	−	2.31080i	−0.0383646	−	0.168086i
$190$	−8.51782	−	10.6810i	−0.617948	−	0.774882i
$191$	−24.4869			−1.77181			−0.885906	−	0.463865i	$-0.846462\pi$
$191$	−24.4869			−1.77181			−0.885906	+	0.463865i	$0.846462\pi$
$192$	−11.9758	−	15.0172i	−0.864282	−	1.08378i
$193$	14.2742	+	6.87409i	1.02748	+	0.494808i	0.870175	−	0.492743i	$-0.164006\pi$
$193$	14.2742	+	6.87409i	1.02748	+	0.494808i	0.157303	+	0.987550i	$0.449720\pi$
$194$	−28.0705	+	35.1993i	−2.01535	+	2.52716i
$195$	4.47725	−	5.61430i	0.320623	−	0.402048i
$196$	6.45924	−	3.11061i	0.461374	−	0.222186i
$197$	−2.83725	−	12.4308i	−0.202146	−	0.885660i	−0.969627	−	0.244588i	$-0.921347\pi$
$197$	−2.83725	−	12.4308i	−0.202146	−	0.885660i	0.767481	−	0.641072i	$-0.221510\pi$
$198$	1.55270	−	6.80284i	0.110346	−	0.483457i
$199$	7.32020	+	3.52522i	0.518915	+	0.249896i	0.674961	−	0.737853i	$-0.264160\pi$
$199$	7.32020	+	3.52522i	0.518915	+	0.249896i	−0.156046	+	0.987750i	$0.549875\pi$
$200$	36.0020	−	17.3377i	2.54573	−	1.22596i
$201$	−1.55189	+	6.79927i	−0.109462	+	0.479584i
$202$	−12.2848			−0.864354
$203$	12.7064	−	1.21267i	0.891811	−	0.0851129i
$204$	25.0615			1.75465
$205$	5.30756	−	23.2539i	0.370696	−	1.62412i
$206$	25.4377	−	12.2501i	1.77233	−	0.853507i
$207$	1.06609	+	0.513403i	0.0740986	+	0.0356840i
$208$	6.43951	−	28.2133i	0.446499	−	1.95624i
$209$	−0.948769	−	4.15683i	−0.0656277	−	0.287534i
$210$	17.8089	−	8.57633i	1.22893	−	0.591823i
$211$	−13.0904	+	16.4149i	−0.901183	+	1.13005i	0.0897871	+	0.995961i	$0.471381\pi$
$211$	−13.0904	+	16.4149i	−0.901183	+	1.13005i	−0.990970	+	0.134086i	$0.957190\pi$
$212$	−16.7319	+	20.9811i	−1.14915	+	1.44099i
$213$	3.36576	+	1.62086i	0.230618	+	0.111060i
$214$	−22.9895	−	28.8279i	−1.57153	−	1.97063i
$215$	5.87102			0.400401
$216$	5.32817	+	6.68131i	0.362536	+	0.454605i
$217$	3.05021	+	13.3639i	0.207062	+	0.907198i
$218$	−3.19302	−	13.9895i	−0.216259	−	0.947491i
$219$	−1.49229	−	1.87127i	−0.100840	−	0.126449i
$220$	41.9988			2.83156
$221$	6.95359	+	8.71952i	0.467749	+	0.586538i
$222$	−16.6623	−	8.02413i	−1.11830	−	0.538544i
$223$	13.2224	−	16.5803i	0.885436	−	1.11030i	−0.107799	−	0.994173i	$-0.534380\pi$
$223$	13.2224	−	16.5803i	0.885436	−	1.11030i	0.993234	−	0.116128i	$-0.0370484\pi$
$224$	24.4077	−	30.6063i	1.63081	−	2.04497i
$225$	−4.21288	+	2.02881i	−0.280858	+	0.135254i
$226$	−6.44172	−	28.2230i	−0.428497	−	1.87737i
$227$	−2.38193	+	10.4359i	−0.158094	+	0.692656i	0.832293	+	0.554335i	$0.187028\pi$
$227$	−2.38193	+	10.4359i	−0.158094	+	0.692656i	−0.990388	+	0.138320i	$0.955830\pi$
$228$	7.65658	+	3.68721i	0.507069	+	0.244192i
$229$	12.6188	−	6.07690i	0.833875	−	0.401573i	0.0323077	−	0.999478i	$-0.489714\pi$
$229$	12.6188	−	6.07690i	0.833875	−	0.401573i	0.801567	+	0.597905i	$0.204000\pi$
$230$	−2.19580	+	9.62044i	−0.144787	+	0.634353i
$231$	6.16905			0.405893
$232$	−39.3781	+	23.8163i	−2.58530	+	1.56361i
$233$	−12.3851			−0.811377			−0.405688	−	0.914011i	$-0.632968\pi$
$233$	−12.3851			−0.811377			−0.405688	+	0.914011i	$0.632968\pi$
$234$	−1.37720	+	6.03391i	−0.0900304	+	0.394449i
$235$	26.0686	−	12.5540i	1.70053	−	0.818931i
$236$	22.9249	+	11.0400i	1.49228	+	0.718645i
$237$	0.836548	−	3.66516i	0.0543396	−	0.238077i
$238$	6.83118	+	29.9294i	0.442800	+	1.94003i
$239$	−8.02168	+	3.86304i	−0.518879	+	0.249879i	−0.674946	−	0.737867i	$-0.735833\pi$
$239$	−8.02168	+	3.86304i	−0.518879	+	0.249879i	0.156066	+	0.987747i	$0.450119\pi$
$240$	−24.3121	+	30.4864i	−1.56934	+	1.96789i
$241$	−16.3041	+	20.4447i	−1.05024	+	1.31696i	−0.103619	+	0.994617i	$0.533042\pi$
$241$	−16.3041	+	20.4447i	−1.05024	+	1.31696i	−0.946623	+	0.322344i	$0.895529\pi$
$242$	−10.2074	−	4.91562i	−0.656156	−	0.315988i
$243$	−0.623490	−	0.781831i	−0.0399969	−	0.0501545i
$244$	−59.8429			−3.83105
$245$	−2.68031	−	3.36100i	−0.171239	−	0.214726i
$246$	4.57445	+	20.0420i	0.291656	+	1.27783i
$247$	0.841529	+	3.68698i	0.0535452	+	0.234597i
$248$	−30.8139	−	38.6394i	−1.95668	−	2.45360i
$249$	10.5949			0.671426
$250$	1.68497	+	2.11289i	0.106567	+	0.133631i
$251$	−3.49262	−	1.68196i	−0.220452	−	0.106164i	0.320398	−	0.947283i	$-0.396183\pi$
$251$	−3.49262	−	1.68196i	−0.220452	−	0.106164i	−0.540851	+	0.841119i	$0.681898\pi$
$252$	−7.66625	+	9.61317i	−0.482928	+	0.605573i
$253$	−1.92018	+	2.40783i	−0.120721	+	0.151379i
$254$	40.7273	−	19.6132i	2.55546	−	1.23064i
$255$	−3.34396	−	14.6508i	−0.209407	−	0.917472i
$256$	−2.46628	+	10.8055i	−0.154142	+	0.675341i
$257$	1.45625	+	0.701292i	0.0908383	+	0.0437454i	0.478751	−	0.877951i	$-0.341090\pi$
$257$	1.45625	+	0.701292i	0.0908383	+	0.0437454i	−0.387913	+	0.921696i	$0.626804\pi$
$258$	−4.55898	+	2.19549i	−0.283830	+	0.136685i
$259$	3.63827	−	15.9403i	0.226071	−	0.990483i
$260$	−37.2516			−2.31025
$261$	4.60793	−	2.78693i	0.285224	−	0.172506i
$262$	−12.2067			−0.754135
$263$	5.04283	−	22.0941i	0.310954	−	1.36238i	−0.541994	−	0.840382i	$-0.682331\pi$
$263$	5.04283	−	22.0941i	0.310954	−	1.36238i	0.852948	−	0.521996i	$-0.174812\pi$
$264$	−20.0394	+	9.65048i	−1.23334	+	0.593946i
$265$	14.4980	+	6.98189i	0.890608	+	0.428894i
$266$	−2.31640	+	10.1488i	−0.142028	+	0.622265i
$267$	−1.26895	−	5.55963i	−0.0776585	−	0.340244i
$268$	32.5959	−	15.6973i	1.99111	−	0.958868i
$269$	−3.25476	+	4.08133i	−0.198446	+	0.248843i	−0.871091	−	0.491122i	$-0.836587\pi$
$269$	−3.25476	+	4.08133i	−0.198446	+	0.248843i	0.672645	+	0.739966i	$0.265158\pi$
$270$	5.19956	−	6.52004i	0.316435	−	0.396797i
$271$	−1.35089	−	0.650556i	−0.0820610	−	0.0395185i	0.392403	−	0.919793i	$-0.371644\pi$
$271$	−1.35089	−	0.650556i	−0.0820610	−	0.0395185i	−0.474464	+	0.880275i	$0.657358\pi$
$272$	−37.7589	−	47.3481i	−2.28947	−	2.87090i
$273$	−5.47175			−0.331166
$274$	36.7896	+	46.1327i	2.22254	+	2.78698i
$275$	−2.70811	−	11.8650i	−0.163305	−	0.715488i
$276$	−1.36590	−	5.98440i	−0.0822175	−	0.360219i
$277$	1.35995	+	1.70532i	0.0817112	+	0.102463i	0.821007	−	0.570918i	$-0.193413\pi$
$277$	1.35995	+	1.70532i	0.0817112	+	0.102463i	−0.739296	+	0.673381i	$0.764841\pi$
$278$	21.6988			1.30141
$279$	3.60577	+	4.52149i	0.215872	+	0.270695i
$280$	−56.7669	−	27.3375i	−3.39247	−	1.63373i
$281$	−10.7411	+	13.4689i	−0.640761	+	0.803489i	−0.991098	−	0.133135i	$-0.957496\pi$
$281$	−10.7411	+	13.4689i	−0.640761	+	0.803489i	0.350337	+	0.936624i	$0.386067\pi$
$282$	−15.5482	+	19.4969i	−0.925884	+	1.16102i
$283$	10.2985	−	4.95949i	0.612182	−	0.294811i	−0.101986	−	0.994786i	$-0.532520\pi$
$283$	10.2985	−	4.95949i	0.612182	−	0.294811i	0.714168	+	0.699975i	$0.246805\pi$
$284$	−4.31228	−	18.8933i	−0.255887	−	1.12111i
$285$	1.13391	−	4.96800i	0.0671672	−	0.294279i
$286$	−14.5132	−	6.98919i	−0.858184	−	0.413280i
$287$	−16.3749	+	7.88572i	−0.966578	+	0.465479i
$288$	3.67518	−	16.1020i	0.216562	−	0.948819i
$289$	6.33927			0.372898
$290$	31.2097	+	32.2924i	1.83269	+	1.89628i
$291$	−16.7931			−0.984428
$292$	−2.76285	+	12.1048i	−0.161683	+	0.708382i
$293$	4.61704	−	2.22345i	0.269730	−	0.129895i	−0.294130	−	0.955765i	$-0.595030\pi$
$293$	4.61704	−	2.22345i	0.269730	−	0.129895i	0.563860	+	0.825870i	$0.309316\pi$
$294$	3.33818	+	1.60758i	0.194686	+	0.0937560i
$295$	3.39509	−	14.8749i	0.197670	−	0.866048i
$296$	13.1176	+	57.4718i	0.762443	+	3.34048i
$297$	2.34497	−	1.12928i	0.136069	−	0.0655273i
$298$	−1.24311	+	1.55881i	−0.0720114	+	0.0902994i
$299$	1.70314	−	2.13567i	0.0984952	−	0.123509i
$300$	21.8545	+	10.5246i	1.26177	+	0.607637i
$301$	−2.78925	−	3.49761i	−0.160770	−	0.201599i
$302$	46.3486			2.66706
$303$	−2.85697	−	3.58253i	−0.164129	−	0.205811i
$304$	−4.56961	−	20.0208i	−0.262085	−	1.14827i
$305$	7.98485	+	34.9839i	0.457211	+	2.00317i
$306$	8.07539	+	10.1262i	0.461639	+	0.578878i
$307$	3.39033			0.193496			0.0967482	−	0.995309i	$-0.469156\pi$
$307$	3.39033			0.193496			0.0967482	+	0.995309i	$0.469156\pi$
$308$	−19.9531	−	25.0204i	−1.13693	−	1.42567i
$309$	9.48826	+	4.56931i	0.539768	+	0.259939i
$310$	−30.0701	+	37.7067i	−1.70787	+	2.14160i
$311$	10.6731	−	13.3836i	0.605213	−	0.758913i	−0.380967	−	0.924589i	$-0.624409\pi$
$311$	10.6731	−	13.3836i	0.605213	−	0.758913i	0.986180	+	0.165675i	$0.0529803\pi$
$312$	17.7744	−	8.55968i	1.00628	−	0.484597i
$313$	0.322250	+	1.41187i	0.0182147	+	0.0798036i	0.983218	−	0.182433i	$-0.0583972\pi$
$313$	0.322250	+	1.41187i	0.0182147	+	0.0798036i	−0.965004	+	0.262236i	$0.915540\pi$
$314$	−0.238202	+	1.04363i	−0.0134425	+	0.0588955i
$315$	6.64274	+	3.19897i	0.374276	+	0.180242i
$316$	−17.5708	+	8.46167i	−0.988437	+	0.476006i
$317$	3.89788	−	17.0777i	0.218927	−	0.959182i	−0.739346	−	0.673326i	$-0.764865\pi$
$317$	3.89788	−	17.0777i	0.218927	−	0.959182i	0.958273	−	0.285856i	$-0.0922779\pi$
$318$	−13.8690			−0.777732
$319$	4.40299	+	13.3065i	0.246520	+	0.745023i
$320$	59.7480			3.34002
$321$	3.06041	−	13.4085i	0.170816	−	0.748392i
$322$	6.77449	−	3.26242i	0.377528	−	0.181808i
$323$	7.13043	+	3.43383i	0.396748	+	0.191064i
$324$	−1.15434	+	5.05749i	−0.0641300	+	0.280972i
$325$	2.40201	+	10.5239i	0.133240	+	0.583762i
$326$	23.9455	−	11.5316i	1.32622	−	0.638674i
$327$	3.33710	−	4.18459i	0.184542	−	0.231409i
$328$	40.8559	−	51.2317i	2.25589	−	2.82880i
$329$	−19.8638	−	9.56589i	−1.09512	−	0.527384i
$330$	13.5330	+	16.9698i	0.744967	+	0.934159i
$331$	10.4276			0.573155			0.286577	−	0.958057i	$-0.407482\pi$
$331$	10.4276			0.573155			0.286577	+	0.958057i	$0.407482\pi$
$332$	−34.2681	−	42.9708i	−1.88071	−	2.35833i
$333$	−1.53499	−	6.72522i	−0.0841168	−	0.368540i
$334$	−6.99119	−	30.6304i	−0.382541	−	1.67602i
$335$	−13.5259	−	16.9609i	−0.738999	−	0.926675i
$336$	29.7123			1.62094
$337$	−20.0771	−	25.1759i	−1.09367	−	1.37142i	−0.922418	−	0.386194i	$-0.873790\pi$
$337$	−20.0771	−	25.1759i	−1.09367	−	1.37142i	−0.171254	−	0.985227i	$-0.554782\pi$
$338$	−18.5282	−	8.92273i	−1.00780	−	0.485333i
$339$	6.73240	−	8.44216i	0.365654	−	0.458515i
$340$	−48.6052	+	60.9489i	−2.63598	+	3.30542i
$341$	−13.5614	+	6.53084i	−0.734393	+	0.353665i
$342$	0.977290	+	4.28179i	0.0528458	+	0.231533i
$343$	−4.42089	+	19.3692i	−0.238705	+	1.04584i
$344$	14.5320	+	6.99824i	0.783513	+	0.377320i
$345$	−3.31621	+	1.59700i	−0.178539	+	0.0859797i
$346$	4.85811	−	21.2848i	0.261173	−	1.14428i
$347$	6.96578			0.373942			0.186971	−	0.982365i	$-0.440133\pi$
$347$	6.96578			0.373942			0.186971	+	0.982365i	$0.440133\pi$
$348$	−26.2070	−	9.67483i	−1.40484	−	0.518625i
$349$	13.9714			0.747871			0.373935	−	0.927455i	$-0.378008\pi$
$349$	13.9714			0.747871			0.373935	+	0.927455i	$0.378008\pi$
$350$	−6.61182	+	28.9683i	−0.353417	+	1.54842i
$351$	−2.07992	+	1.00163i	−0.111018	+	0.0534633i
$352$	38.7297	+	18.6513i	2.06430	+	0.994115i
$353$	−5.75044	+	25.1943i	−0.306065	+	1.34096i	0.554740	+	0.832024i	$0.312818\pi$
$353$	−5.75044	+	25.1943i	−0.306065	+	1.34096i	−0.860805	+	0.508935i	$0.830039\pi$
$354$	2.92614	+	12.8203i	0.155523	+	0.681390i
$355$	−10.4696	+	5.04189i	−0.555668	+	0.267596i
$356$	−18.4444	+	23.1286i	−0.977554	+	1.22581i
$357$	−7.13943	+	8.95257i	−0.377859	+	0.473820i
$358$	26.0351	+	12.5379i	1.37600	+	0.662646i
$359$	−10.9382	−	13.7160i	−0.577295	−	0.723905i	0.404354	−	0.914603i	$-0.367496\pi$
$359$	−10.9382	−	13.7160i	−0.577295	−	0.723905i	−0.981649	+	0.190698i	$0.938925\pi$
$360$	−26.5824			−1.40102
$361$	−10.1731	−	12.7566i	−0.535425	−	0.671402i
$362$	12.2968	+	53.8758i	0.646305	+	2.83165i
$363$	−0.940341	−	4.11990i	−0.0493551	−	0.216239i
$364$	17.6978	+	22.1923i	0.927616	+	1.16319i
$365$	7.44509			0.389694
$366$	−19.2828	−	24.1798i	−1.00793	−	1.26390i
$367$	−26.8154	−	12.9136i	−1.39975	−	0.674086i	−0.426643	−	0.904420i	$-0.640304\pi$
$367$	−26.8154	−	12.9136i	−1.39975	−	0.674086i	−0.973112	+	0.230334i	$0.926018\pi$
$368$	−9.24827	+	11.5970i	−0.482100	+	0.604534i
$369$	−4.78087	+	5.99502i	−0.248882	+	0.312088i
$370$	51.8299	−	24.9600i	2.69451	−	1.29761i
$371$	−2.72844	−	11.9541i	−0.141654	−	0.620625i
$372$	6.67578	−	29.2485i	0.346123	−	1.51647i
$373$	−17.3846	−	8.37200i	−0.900142	−	0.433485i	−0.0742017	−	0.997243i	$-0.523641\pi$
$373$	−17.3846	−	8.37200i	−0.900142	−	0.433485i	−0.825940	+	0.563758i	$0.809355\pi$
$374$	−30.3719	+	14.6263i	−1.57049	+	0.756309i
$375$	−0.224308	+	0.982756i	−0.0115832	+	0.0507493i
$376$	79.4894			4.09936
$377$	−3.90532	−	11.8025i	−0.201134	−	0.607859i
$378$	−6.35450			−0.326840
$379$	1.91129	−	8.37391i	0.0981763	−	0.430139i	−0.901822	−	0.432108i	$-0.857770\pi$
$379$	1.91129	−	8.37391i	0.0981763	−	0.430139i	0.999998	+	0.00196965i	$0.000626959\pi$
$380$	−23.8167	+	11.4695i	−1.22177	+	0.588373i
$381$	15.1913	+	7.31574i	0.778273	+	0.374797i
$382$	−14.6082	+	64.0026i	−0.747419	+	3.27466i
$383$	6.29552	+	27.5825i	0.321686	+	1.40940i	0.834552	+	0.550930i	$0.185727\pi$
$383$	6.29552	+	27.5825i	0.321686	+	1.40940i	−0.512865	+	0.858469i	$0.671416\pi$
$384$	−16.6347	+	8.01084i	−0.848885	+	0.408802i
$385$	−11.9645	+	15.0030i	−0.609767	+	0.764623i
$386$	26.4827	−	33.2082i	1.34793	−	1.69025i
$387$	−1.70050	−	0.818919i	−0.0864414	−	0.0416280i
$388$	54.3153	+	68.1093i	2.75744	+	3.45772i
$389$	−27.1843			−1.37830			−0.689149	−	0.724619i	$-0.742016\pi$
$389$	−27.1843			−1.37830			−0.689149	+	0.724619i	$0.742016\pi$
$390$	−12.0033	−	15.0517i	−0.607813	−	0.762174i
$391$	−1.27204	−	5.57316i	−0.0643297	−	0.281847i
$392$	−2.62802	−	11.5141i	−0.132735	−	0.581550i
$393$	−2.83882	−	3.55977i	−0.143200	−	0.179567i
$394$	−34.1836			−1.72215
$395$	7.29115	+	9.14281i	0.366857	+	0.460025i
$396$	−12.1647	−	5.85819i	−0.611297	−	0.294385i
$397$	3.09017	−	3.87495i	0.155091	−	0.194478i	−0.698215	−	0.715888i	$-0.746022\pi$
$397$	3.09017	−	3.87495i	0.155091	−	0.194478i	0.853306	+	0.521410i	$0.174594\pi$
$398$	13.5810	−	17.0301i	0.680756	−	0.853641i
$399$	−3.49835	+	1.68471i	−0.175136	+	0.0843412i
$400$	−13.0432	−	57.1462i	−0.652162	−	2.85731i
$401$	−1.38397	+	6.06358i	−0.0691123	+	0.302801i	−0.997657	−	0.0684210i	$-0.978204\pi$
$401$	−1.38397	+	6.06358i	−0.0691123	+	0.302801i	0.928544	+	0.371222i	$0.121061\pi$
$402$	16.8458	+	8.11249i	0.840190	+	0.404614i
$403$	12.0286	−	5.79266i	0.599186	−	0.288553i
$404$	−5.28945	+	23.1746i	−0.263160	+	1.15298i
$405$	3.11062			0.154568
$406$	4.41061	−	33.9346i	0.218895	−	1.68415i
$407$	17.9540			0.889946
$408$	9.18677	−	40.2499i	0.454813	−	1.99267i
$409$	−4.17933	+	2.01266i	−0.206655	+	0.0995196i	−0.534348	−	0.845264i	$-0.679443\pi$
$409$	−4.17933	+	2.01266i	−0.206655	+	0.0995196i	0.327694	+	0.944784i	$0.393729\pi$
$410$	−57.6135	−	27.7452i	−2.84533	−	1.37024i
$411$	−4.89751	+	21.4574i	−0.241577	+	1.05842i
$412$	−12.1566	−	53.2613i	−0.598910	−	2.62400i
$413$	−10.4745	+	5.04427i	−0.515418	+	0.248212i
$414$	1.97790	−	2.48021i	0.0972087	−	0.121896i
$415$	−20.5482	+	25.7666i	−1.00867	+	1.26483i
$416$	−34.3521	−	16.5431i	−1.68425	−	0.811092i
$417$	5.04632	+	6.32789i	0.247119	+	0.309878i
$418$	−11.4309			−0.559103
$419$	8.52181	+	10.6860i	0.416318	+	0.522046i	0.945131	−	0.326693i	$-0.105934\pi$
$419$	8.52181	+	10.6860i	0.416318	+	0.522046i	−0.528813	+	0.848738i	$0.677363\pi$
$420$	−8.51081	−	37.2883i	−0.415285	−	1.81948i
$421$	2.64867	+	11.6046i	0.129088	+	0.565573i	0.997559	+	0.0698322i	$0.0222464\pi$
$421$	2.64867	+	11.6046i	0.129088	+	0.565573i	−0.868470	+	0.495741i	$0.834896\pi$
$422$	35.0949	+	44.0077i	1.70840	+	2.14226i
$423$	−9.30167			−0.452263
$424$	27.5633	+	34.5633i	1.33859	+	1.67854i
$425$	20.3527	+	9.80135i	0.987252	+	0.475435i
$426$	6.24444	−	7.83028i	0.302544	−	0.379378i
$427$	17.0479	−	21.3773i	0.825003	−	1.03452i
$428$	−64.2809	+	30.9560i	−3.10713	+	1.49632i
$429$	−1.33701	−	5.85781i	−0.0645513	−	0.282818i
$430$	3.50248	−	15.3454i	0.168904	−	0.740019i
$431$	20.4808	+	9.86302i	0.986524	+	0.475085i	0.856344	−	0.516405i	$-0.172730\pi$
$431$	20.4808	+	9.86302i	0.986524	+	0.475085i	0.130180	+	0.991490i	$0.458444\pi$
$432$	11.2942	−	5.43900i	0.543393	−	0.261684i
$433$	1.22623	−	5.37245i	0.0589287	−	0.258184i	−0.936879	−	0.349653i	$-0.886299\pi$
$433$	1.22623	−	5.37245i	0.0589287	−	0.258184i	0.995808	+	0.0914698i	$0.0291565\pi$
$434$	36.7494			1.76403
$435$	−2.15906	+	16.6115i	−0.103519	+	0.796459i
$436$	−27.7653			−1.32972
$437$	0.431339	−	1.88982i	0.0206337	−	0.0904023i
$438$	−5.78128	+	2.78412i	−0.276240	+	0.133030i
$439$	−18.2571	−	8.79215i	−0.871363	−	0.419626i	−0.0559006	−	0.998436i	$-0.517803\pi$
$439$	−18.2571	−	8.79215i	−0.871363	−	0.419626i	−0.815462	+	0.578810i	$0.803517\pi$
$440$	15.3955	−	67.4520i	0.733950	−	3.21565i
$441$	0.307525	+	1.34735i	0.0146440	+	0.0641597i
$442$	26.9389	−	12.9731i	1.28135	−	0.617067i
$443$	21.1350	−	26.5024i	1.00415	−	1.25917i	0.0385212	−	0.999258i	$-0.487735\pi$
$443$	21.1350	−	26.5024i	1.00415	−	1.25917i	0.965633	−	0.259911i	$-0.0836933\pi$
$444$	−22.3114	+	27.9776i	−1.05885	+	1.32776i
$445$	15.9820	+	7.69650i	0.757617	+	0.364849i
$446$	−35.4487	−	44.4512i	−1.67854	−	2.10483i
$447$	−0.743685			−0.0351751
$448$	−28.3855	−	35.5943i	−1.34109	−	1.68167i
$449$	−7.17733	−	31.4459i	−0.338719	−	1.48403i	−0.801737	−	0.597677i	$-0.796091\pi$
$449$	−7.17733	−	31.4459i	−0.338719	−	1.48403i	0.463018	−	0.886349i	$-0.346766\pi$
$450$	2.78953	+	12.2217i	0.131499	+	0.576137i
$451$	−12.4432	−	15.6033i	−0.585930	−	0.734733i
$452$	−56.0148			−2.63472
$453$	10.7789	+	13.5163i	0.506437	+	0.635052i
$454$	25.8558	+	12.4515i	1.21347	+	0.584378i
$455$	10.6121	−	13.3072i	0.497504	−	0.623851i
$456$	8.72851	−	10.9452i	0.408750	−	0.512556i
$457$	23.5438	−	11.3381i	1.10133	−	0.530375i	0.207257	−	0.978287i	$-0.433546\pi$
$457$	23.5438	−	11.3381i	1.10133	−	0.530375i	0.894078	+	0.447912i	$0.147832\pi$
$458$	−8.35546	−	36.6076i	−0.390425	−	1.71056i
$459$	−1.07502	+	4.70995i	−0.0501774	+	0.219842i
$460$	17.2030	+	8.28453i	0.802095	+	0.386268i
$461$	11.2947	−	5.43923i	0.526046	−	0.253330i	−0.151960	−	0.988387i	$-0.548559\pi$
$461$	11.2947	−	5.43923i	0.526046	−	0.253330i	0.678006	+	0.735056i	$0.262844\pi$
$462$	3.68027	−	16.1243i	0.171222	−	0.750171i
$463$	−38.0989			−1.77061			−0.885303	−	0.465014i	$-0.846049\pi$
$463$	−38.0989			−1.77061			−0.885303	+	0.465014i	$0.846049\pi$
$464$	21.2064	+	64.0890i	0.984482	+	2.97526i
$465$	−17.9893			−0.834236
$466$	−7.38860	+	32.3716i	−0.342270	+	1.49958i
$467$	6.22496	−	2.99778i	0.288057	−	0.138721i	−0.284276	−	0.958743i	$-0.591753\pi$
$467$	6.22496	−	2.99778i	0.288057	−	0.138721i	0.572332	+	0.820022i	$0.306039\pi$
$468$	10.7897	+	5.19603i	0.498753	+	0.240187i
$469$	−3.67834	+	16.1159i	−0.169850	+	0.744161i
$470$	−17.2611	−	75.6259i	−0.796196	−	3.48836i
$471$	−0.359744	+	0.173243i	−0.0165761	+	0.00798264i
$472$	26.1344	−	32.7714i	1.20293	−	1.50843i
$473$	3.06284	−	3.84068i	0.140829	−	0.176595i
$474$	−9.08072	−	4.37304i	−0.417091	−	0.200861i
$475$	4.77596	+	5.98886i	0.219136	+	0.274788i
$476$	59.4015			2.72266
$477$	−3.22539	−	4.04451i	−0.147681	−	0.185186i
$478$	5.31150	+	23.2712i	0.242942	+	1.06440i
$479$	3.38908	+	14.8485i	0.154851	+	0.678446i	0.991434	+	0.130607i	$0.0416925\pi$
$479$	3.38908	+	14.8485i	0.154851	+	0.678446i	−0.836583	+	0.547840i	$0.815450\pi$
$480$	32.0319	+	40.1668i	1.46205	+	1.83335i
$481$	−15.9246			−0.726101
$482$	43.7108	+	54.8116i	1.99097	+	2.49660i
$483$	2.52689	+	1.21689i	0.114977	+	0.0553702i
$484$	−13.6681	+	17.1392i	−0.621275	+	0.779054i
$485$	32.5691	−	40.8404i	1.47889	−	1.85447i
$486$	−2.41546	+	1.16323i	−0.109568	+	0.0527650i
$487$	7.04525	+	30.8672i	0.319251	+	1.39873i	0.838871	+	0.544331i	$0.183216\pi$
$487$	7.04525	+	30.8672i	0.319251	+	1.39873i	−0.519620	+	0.854397i	$0.673927\pi$
$488$	−21.9366	+	96.1104i	−0.993022	+	4.35071i
$489$	8.93169	+	4.30127i	0.403905	+	0.194510i
$490$	−10.3838	+	5.00057i	−0.469092	+	0.225903i
$491$	−2.38715	+	10.4588i	−0.107731	+	0.471998i	0.892067	+	0.451902i	$0.149254\pi$
$491$	−2.38715	+	10.4588i	−0.107731	+	0.471998i	−0.999798	+	0.0200962i	$0.993603\pi$
$492$	39.7777			1.79332
$493$	−24.4061	−	9.00999i	−1.09920	−	0.405789i
$494$	10.1388			0.456168
$495$	−1.80154	+	7.89308i	−0.0809733	+	0.354767i
$496$	−65.3167	+	31.4549i	−2.93281	+	1.41237i
$497$	7.97763	+	3.84182i	0.357846	+	0.172329i
$498$	6.32062	−	27.6924i	0.283234	−	1.24093i
$499$	2.17395	+	9.52472i	0.0973196	+	0.426385i	0.999992	−	0.00394299i	$-0.00125509\pi$
$499$	2.17395	+	9.52472i	0.0973196	+	0.426385i	−0.902673	+	0.430328i	$0.858398\pi$
$500$	4.71135	−	2.26887i	0.210698	−	0.101467i
$501$	7.30666	−	9.16227i	0.326438	−	0.409340i
$502$	−6.47980	+	8.12541i	−0.289208	+	0.362655i
$503$	21.8843	+	10.5389i	0.975771	+	0.469907i	0.852649	−	0.522485i	$-0.174995\pi$
$503$	21.8843	+	10.5389i	0.975771	+	0.469907i	0.123123	+	0.992391i	$0.460709\pi$
$504$	12.6290	+	15.8362i	0.562540	+	0.705403i
$505$	14.2536			0.634275
$506$	5.14793	+	6.45530i	0.228853	+	0.286973i
$507$	−1.70689	−	7.47836i	−0.0758055	−	0.332126i
$508$	−19.4634	−	85.2747i	−0.863548	−	3.78345i
$509$	−2.52048	−	3.16058i	−0.111718	−	0.140090i	0.722828	−	0.691028i	$-0.242842\pi$
$509$	−2.52048	−	3.16058i	−0.111718	−	0.140090i	−0.834547	+	0.550937i	$0.814270\pi$
$510$	−40.2885			−1.78400
$511$	−3.53707	−	4.43534i	−0.156471	−	0.196208i
$512$	−6.49796	−	3.12925i	−0.287172	−	0.138295i
$513$	−1.02139	+	1.28078i	−0.0450955	+	0.0565479i
$514$	2.70175	−	3.38789i	0.119169	−	0.149433i
$515$	−29.5144	+	14.2134i	−1.30056	+	0.626316i
$516$	2.17872	+	9.54559i	0.0959127	+	0.420221i
$517$	5.38715	−	23.6027i	0.236927	−	1.03804i
$518$	−39.4934	−	19.0190i	−1.73524	−	0.835649i
$519$	7.33695	−	3.53329i	0.322056	−	0.155094i
$520$	−13.6553	+	59.8278i	−0.598825	+	2.62362i
$521$	−20.3240			−0.890412			−0.445206	−	0.895428i	$-0.646870\pi$
$521$	−20.3240			−0.890412			−0.445206	+	0.895428i	$0.646870\pi$
$522$	−4.53536	−	13.7066i	−0.198507	−	0.599920i
$523$	0.181906			0.00795418			0.00397709	−	0.999992i	$-0.498734\pi$
$523$	0.181906			0.00795418			0.00397709	+	0.999992i	$0.498734\pi$
$524$	−5.25585	+	23.0274i	−0.229603	+	1.00596i
$525$	−9.98549	+	4.80876i	−0.435803	+	0.209871i
$526$	−54.7398	−	26.3613i	−2.38677	−	1.14941i
$527$	6.21703	−	27.2386i	0.270818	−	1.18653i
$528$	7.26012	+	31.8087i	0.315956	+	1.38430i
$529$	19.4608	−	9.37183i	0.846122	−	0.407471i
$530$	26.8980	−	33.7290i	1.16837	−	1.46509i
$531$	−3.05818	+	3.83484i	−0.132714	+	0.166418i
$532$	18.1479	+	8.73955i	0.786810	+	0.378908i
$533$	11.0368	+	13.8397i	0.478056	+	0.599463i
$534$	−15.2885			−0.661597
$535$	26.6738	+	33.4479i	1.15321	+	1.44608i
$536$	−13.2620	−	58.1047i	−0.572832	−	2.50974i
$537$	2.39845	+	10.5083i	0.103501	+	0.453466i
$538$	8.72587	+	10.9419i	0.376199	+	0.471739i
$539$	−3.59696			−0.154932
$540$	−10.0609	−	12.6160i	−0.432954	−	0.542907i
$541$	24.3124	+	11.7082i	1.04527	+	0.503376i	0.876059	−	0.482203i	$-0.160163\pi$
$541$	24.3124	+	11.7082i	1.04527	+	0.503376i	0.169212	+	0.985580i	$0.445878\pi$
$542$	−2.50629	+	3.14279i	−0.107654	+	0.134994i
$543$	−12.8517	+	16.1155i	−0.551518	+	0.691582i
$544$	−71.8887	+	34.6198i	−3.08220	+	1.48431i
$545$	3.70474	+	16.2315i	0.158694	+	0.695282i
$546$	−3.26429	+	14.3018i	−0.139699	+	0.612059i
$547$	−7.87494	−	3.79237i	−0.336708	−	0.162150i	0.257887	−	0.966175i	$-0.416974\pi$
$547$	−7.87494	−	3.79237i	−0.336708	−	0.162150i	−0.594596	+	0.804025i	$0.702688\pi$
$548$	102.867	−	49.5383i	4.39427	−	2.11617i
$549$	2.56697	−	11.2466i	0.109556	−	0.479994i
$550$	−32.6277			−1.39125
$551$	−6.13075	−	6.34346i	−0.261179	−	0.270240i
$552$	−10.1119			−0.430392
$553$	1.98281	−	8.68727i	0.0843177	−	0.369420i
$554$	5.26857	−	2.53721i	0.223840	−	0.107796i
$555$	19.3326	+	9.31009i	0.820623	+	0.395191i
$556$	9.34285	−	40.9337i	0.396225	−	1.73598i
$557$	6.30376	+	27.6186i	0.267099	+	1.17024i	0.913371	+	0.407129i	$0.133470\pi$
$557$	6.30376	+	27.6186i	0.267099	+	1.17024i	−0.646272	+	0.763107i	$0.723673\pi$
$558$	13.9691	−	6.72717i	0.591360	−	0.284784i
$559$	−2.71664	+	3.40656i	−0.114902	+	0.144082i
$560$	−57.6252	+	72.2597i	−2.43511	+	3.05353i
$561$	−11.3287	−	5.45562i	−0.478299	−	0.230337i
$562$	28.7965	+	36.1097i	1.21471	+	1.52319i
$563$	−1.24481			−0.0524623			−0.0262312	−	0.999656i	$-0.508351\pi$
$563$	−1.24481			−0.0524623			−0.0262312	+	0.999656i	$0.508351\pi$
$564$	30.0852	+	37.7257i	1.26682	+	1.58854i
$565$	7.47408	+	32.7461i	0.314437	+	1.37764i
$566$	−6.81907	−	29.8763i	−0.286627	−	1.25579i
$567$	−1.47782	−	1.85312i	−0.0620624	−	0.0778238i
$568$	−31.9243			−1.33951
$569$	−5.14541	−	6.45214i	−0.215707	−	0.270488i	0.662192	−	0.749334i	$-0.269626\pi$
$569$	−5.14541	−	6.45214i	−0.215707	−	0.270488i	−0.877899	+	0.478847i	$0.841055\pi$
$570$	−12.3086	−	5.92752i	−0.515551	−	0.248276i
$571$	17.3342	−	21.7364i	0.725415	−	0.909642i	−0.273216	−	0.961953i	$-0.588087\pi$
$571$	17.3342	−	21.7364i	0.725415	−	0.909642i	0.998631	+	0.0523110i	$0.0166587\pi$
$572$	−19.4337	+	24.3691i	−0.812563	+	1.01892i
$573$	−22.0620	+	10.6245i	−0.921651	+	0.443844i
$574$	10.8425	+	47.5041i	0.452557	+	1.98278i
$575$	1.23119	−	5.39420i	0.0513442	−	0.224954i
$576$	−17.3056	−	8.33394i	−0.721067	−	0.347247i
$577$	−6.48400	+	3.12253i	−0.269932	+	0.129993i	−0.563954	−	0.825806i	$-0.690721\pi$
$577$	−6.48400	+	3.12253i	−0.269932	+	0.129993i	0.294022	+	0.955799i	$0.405006\pi$
$578$	3.78182	−	16.5692i	0.157303	−	0.689190i
$579$	15.8432			0.658419
$580$	74.3559	−	44.9712i	3.08746	−	1.86733i
$581$	25.1124			1.04184
$582$	−10.0182	+	43.8928i	−0.415270	+	1.81942i
$583$	12.1308	−	5.84190i	0.502407	−	0.241947i
$584$	18.4281	+	8.87453i	0.762562	+	0.367231i
$585$	1.59791	−	7.00092i	0.0660656	−	0.289452i
$586$	−3.05714	−	13.3942i	−0.126289	−	0.553310i
$587$	−7.62256	+	3.67083i	−0.314617	+	0.151511i	−0.584527	−	0.811374i	$-0.698720\pi$
$587$	−7.62256	+	3.67083i	−0.314617	+	0.151511i	0.269911	+	0.962885i	$0.413006\pi$
$588$	4.46993	−	5.60512i	0.184337	−	0.231151i
$589$	5.90691	−	7.40703i	0.243390	−	0.305201i
$590$	−36.8537	−	17.7478i	−1.51724	−	0.730666i
$591$	−7.94981	−	9.96875i	−0.327012	−	0.410060i
$592$	86.4728			3.55401
$593$	−17.9522	−	22.5114i	−0.737210	−	0.924433i	0.261963	−	0.965078i	$-0.415630\pi$
$593$	−17.9522	−	22.5114i	−0.737210	−	0.924433i	−0.999174	+	0.0406452i	$0.987059\pi$
$594$	−1.55270	−	6.80284i	−0.0637082	−	0.279124i
$595$	−7.92596	−	34.7259i	−0.324933	−	1.42362i
$596$	2.40537	+	3.01623i	0.0985277	+	0.123550i
$597$	8.12481			0.332526
$598$	−4.56606	−	5.72565i	−0.186720	−	0.234139i
$599$	2.23432	+	1.07599i	0.0912920	+	0.0439639i	0.478973	−	0.877830i	$-0.341009\pi$
$599$	2.23432	+	1.07599i	0.0912920	+	0.0439639i	−0.387681	+	0.921794i	$0.626724\pi$
$600$	24.9142	−	31.2414i	1.01712	−	1.27542i
$601$	−24.7528	+	31.0390i	−1.00969	+	1.26611i	−0.0460366	+	0.998940i	$0.514659\pi$
$601$	−24.7528	+	31.0390i	−1.00969	+	1.26611i	−0.963650	+	0.267167i	$0.913912\pi$
$602$	−10.8058	+	5.20382i	−0.440413	+	0.212092i
$603$	1.55189	+	6.79927i	0.0631979	+	0.276888i
$604$	19.9563	−	87.4341i	0.812009	−	3.55764i
$605$	11.8433	+	5.70341i	0.481497	+	0.231877i
$606$	−11.0682	+	5.33016i	−0.449615	+	0.216523i
$607$	−7.86688	+	34.4671i	−0.319307	+	1.39898i	0.519465	+	0.854492i	$0.326131\pi$
$607$	−7.86688	+	34.4671i	−0.319307	+	1.39898i	−0.838772	+	0.544483i	$0.816726\pi$
$608$	−27.0564			−1.09728
$609$	10.9219	−	6.60566i	0.442576	−	0.267675i
$610$	96.2026			3.89513
$611$	−4.77824	+	20.9348i	−0.193307	+	0.846933i
$612$	22.5796	−	10.8738i	0.912726	−	0.439546i
$613$	−7.29240	−	3.51183i	−0.294537	−	0.141842i	0.280780	−	0.959772i	$-0.409407\pi$
$613$	−7.29240	−	3.51183i	−0.294537	−	0.141842i	−0.575317	+	0.817931i	$0.695121\pi$
$614$	2.02257	−	8.86146i	0.0816243	−	0.357619i
$615$	−5.30756	−	23.2539i	−0.214021	−	0.937689i
$616$	−47.4981	+	22.8739i	−1.91375	+	0.921615i
$617$	17.0599	−	21.3924i	0.686805	−	0.861227i	−0.309156	−	0.951011i	$-0.600046\pi$
$617$	17.0599	−	21.3924i	0.686805	−	0.861227i	0.995961	+	0.0897847i	$0.0286179\pi$
$618$	17.6034	−	22.0740i	0.708113	−	0.887946i
$619$	−24.4911	−	11.7943i	−0.984382	−	0.474053i	−0.128772	−	0.991674i	$-0.541103\pi$
$619$	−24.4911	−	11.7943i	−0.984382	−	0.474053i	−0.855610	+	0.517621i	$0.826818\pi$
$620$	58.1845	+	72.9611i	2.33675	+	2.93019i
$621$	1.18327			0.0474832
$622$	−28.6140	−	35.8809i	−1.14732	−	1.43869i
$623$	−3.00770	−	13.1776i	−0.120501	−	0.527950i
$624$	−6.43951	−	28.2133i	−0.257787	−	1.12944i
$625$	−16.5320	−	20.7305i	−0.661280	−	0.829219i
$626$	3.88251			0.155176
$627$	−2.65839	−	3.33352i	−0.106166	−	0.133128i
$628$	1.86619	+	0.898710i	0.0744691	+	0.0358624i
$629$	−20.7781	+	26.0550i	−0.828479	+	1.03888i
$630$	12.3242	−	15.4540i	0.491006	−	0.615702i
$631$	−17.7488	+	8.54737i	−0.706568	+	0.340265i	−0.752421	−	0.658683i	$-0.771114\pi$
$631$	−17.7488	+	8.54737i	−0.706568	+	0.340265i	0.0458525	+	0.998948i	$0.485400\pi$
$632$	7.14890	+	31.3214i	0.284368	+	1.24590i
$633$	−4.67192	+	20.4690i	−0.185692	+	0.813571i
$634$	−42.3115	−	20.3761i	−1.68040	−	0.809240i
$635$	−47.2543	+	22.7565i	−1.87523	+	0.903062i
$636$	−5.97155	+	26.1631i	−0.236787	+	1.03743i
$637$	3.19040			0.126408
$638$	37.4066	−	3.57002i	1.48094	−	0.141338i
$639$	3.73571			0.147782
$640$	12.7797	−	55.9917i	0.505164	−	2.21327i
$641$	−0.252515	+	0.121605i	−0.00997374	+	0.00480310i	−0.438864	−	0.898554i	$-0.644619\pi$
$641$	−0.252515	+	0.121605i	−0.00997374	+	0.00480310i	0.428890	+	0.903357i	$0.358905\pi$
$642$	−33.2208	−	15.9983i	−1.31112	−	0.631402i
$643$	10.4808	−	45.9192i	0.413321	−	1.81088i	−0.154817	−	0.987943i	$-0.549479\pi$
$643$	10.4808	−	45.9192i	0.413321	−	1.81088i	0.568137	−	0.822934i	$-0.307664\pi$
$644$	−3.23750	−	14.1844i	−0.127575	−	0.558944i
$645$	5.28961	−	2.54734i	0.208278	−	0.100302i
$646$	13.2290	−	16.5886i	0.520487	−	0.652670i
$647$	−0.681877	+	0.855046i	−0.0268073	+	0.0336153i	−0.795054	−	0.606538i	$-0.792558\pi$
$647$	−0.681877	+	0.855046i	−0.0268073	+	0.0336153i	0.768247	+	0.640153i	$0.221129\pi$
$648$	7.69942	+	3.70785i	0.302462	+	0.145658i
$649$	−7.95959	−	9.98101i	−0.312441	−	0.391789i
$650$	28.9398			1.13511
$651$	8.54651	+	10.7170i	0.334964	+	0.420032i
$652$	−11.4435	−	50.1371i	−0.448161	−	1.96352i
$653$	6.63281	+	29.0602i	0.259562	+	1.13722i	0.921721	+	0.387852i	$0.126783\pi$
$653$	6.63281	+	29.0602i	0.259562	+	1.13722i	−0.662160	+	0.749363i	$0.730360\pi$
$654$	−8.94664	−	11.2187i	−0.349841	−	0.438687i
$655$	14.1630			0.553395
$656$	−59.9311	−	75.1513i	−2.33992	−	2.93416i
$657$	−2.15642	−	1.03848i	−0.0841299	−	0.0405148i
$658$	−36.8529	+	46.2121i	−1.43668	+	1.80153i
$659$	−20.7854	+	26.0640i	−0.809683	+	1.01531i	0.189756	+	0.981831i	$0.439230\pi$
$659$	−20.7854	+	26.0640i	−0.809683	+	1.01531i	−0.999439	+	0.0334791i	$0.989341\pi$
$660$	37.8396	−	18.2226i	1.47290	−	0.709313i
$661$	−0.544903	−	2.38738i	−0.0211943	−	0.0928581i	0.963225	−	0.268698i	$-0.0865932\pi$
$661$	−0.544903	−	2.38738i	−0.0211943	−	0.0928581i	−0.984419	+	0.175839i	$0.943736\pi$
$662$	6.22082	−	27.2552i	0.241779	−	1.05930i
$663$	10.0482	+	4.83897i	0.390241	+	0.187930i
$664$	−81.5748	+	39.2844i	−3.16572	+	1.52453i
$665$	2.68764	−	11.7753i	0.104222	−	0.456627i
$666$	−18.4937			−0.716617
$667$	−0.821302	+	6.31898i	−0.0318009	+	0.244672i
$668$	−60.7929			−2.35215
$669$	4.71901	−	20.6753i	0.182447	−	0.799355i
$670$	−52.4007	+	25.2348i	−2.02442	+	0.974907i
$671$	27.0512	+	13.0272i	1.04430	+	0.502908i
$672$	8.71102	−	38.1655i	0.336035	−	1.47226i
$673$	−2.49804	−	10.9446i	−0.0962924	−	0.421884i	0.903688	−	0.428192i	$-0.140849\pi$
$673$	−2.49804	−	10.9446i	−0.0962924	−	0.421884i	−0.999980	+	0.00630766i	$0.997992\pi$
$674$	−77.7809	+	37.4573i	−2.99601	+	1.44280i
$675$	−2.91540	+	3.65580i	−0.112214	+	0.140712i
$676$	−24.8100	+	31.1107i	−0.954229	+	1.19657i
$677$	4.61715	+	2.22350i	0.177451	+	0.0854561i	0.520500	−	0.853861i	$-0.325745\pi$
$677$	4.61715	+	2.22350i	0.177451	+	0.0854561i	−0.343049	+	0.939318i	$0.611460\pi$
$678$	−18.0493	−	22.6331i	−0.693179	−	0.869219i
$679$	−39.8035			−1.52752
$680$	80.0697	+	100.404i	3.07053	+	3.85032i
$681$	2.38193	+	10.4359i	0.0912757	+	0.399905i
$682$	8.97961	+	39.3422i	0.343847	+	1.50649i
$683$	18.4315	+	23.1123i	0.705260	+	0.884368i	0.997404	−	0.0720063i	$-0.0229402\pi$
$683$	18.4315	+	23.1123i	0.705260	+	0.884368i	−0.292144	+	0.956374i	$0.594369\pi$
$684$	8.49816			0.324935
$685$	−42.6855	−	53.5260i	−1.63093	−	2.04512i
$686$	47.9887	+	23.1101i	1.83222	+	0.882349i
$687$	8.73249	−	10.9502i	0.333165	−	0.417776i
$688$	14.7517	−	18.4981i	0.562404	−	0.705232i
$689$	−10.7597	+	5.18158i	−0.409911	+	0.197403i
$690$	2.19580	+	9.62044i	0.0835928	+	0.366244i
$691$	−9.83685	+	43.0981i	−0.374211	+	1.63953i	0.340599	+	0.940209i	$0.389370\pi$
$691$	−9.83685	+	43.0981i	−0.374211	+	1.63953i	−0.714810	+	0.699319i	$0.753487\pi$
$692$	−38.0608	−	18.3291i	−1.44685	−	0.696769i
$693$	5.55812	−	2.67665i	0.211135	−	0.101677i
$694$	4.15557	−	18.2068i	0.157743	−	0.691119i
$695$	−25.1763			−0.954992
$696$	−25.1449	+	38.5432i	−0.953116	+	1.46098i
$697$	37.0443			1.40315
$698$	8.33491	−	36.5176i	0.315481	−	1.38221i
$699$	−11.1586	+	5.37371i	−0.422058	+	0.203252i
$700$	51.8003	+	24.9457i	1.95787	+	0.942859i
$701$	5.71682	−	25.0470i	0.215921	−	0.946013i	−0.744535	−	0.667583i	$-0.767329\pi$
$701$	5.71682	−	25.0470i	0.215921	−	0.946013i	0.960457	−	0.278430i	$-0.0898139\pi$
$702$	1.37720	+	6.03391i	0.0519791	+	0.227735i
$703$	−10.1814	+	4.90308i	−0.383997	+	0.184923i
$704$	31.1698	−	39.0857i	1.17475	−	1.47310i
$705$	18.0400	−	22.6215i	0.679426	−	0.851974i
$706$	62.4210	+	30.0604i	2.34925	+	1.13134i
$707$	−6.77168	−	8.49142i	−0.254675	−	0.319353i
$708$	25.4447			0.956269
$709$	11.3053	+	14.1764i	0.424579	+	0.532405i	0.947406	−	0.320033i	$-0.103694\pi$
$709$	11.3053	+	14.1764i	0.424579	+	0.532405i	−0.522827	+	0.852439i	$0.675123\pi$
$710$	6.93236	+	30.3727i	0.260167	+	1.13987i
$711$	−0.836548	−	3.66516i	−0.0313730	−	0.137454i
$712$	30.3844	+	38.1009i	1.13871	+	1.42789i
$713$	−6.84312			−0.256277
$714$	19.1405	+	24.0015i	0.716317	+	0.898233i
$715$	16.8391	+	8.10929i	0.629747	+	0.303270i
$716$	34.8619	−	43.7155i	1.30285	−	1.63372i
$717$	−5.55118	+	6.96096i	−0.207312	+	0.259962i
$718$	−42.3756	+	20.4070i	−1.58144	+	0.761583i
$719$	−1.22528	−	5.36832i	−0.0456954	−	0.200205i	0.946928	−	0.321447i	$-0.104169\pi$
$719$	−1.22528	−	5.36832i	−0.0456954	−	0.200205i	−0.992623	+	0.121243i	$0.961312\pi$
$720$	−8.67687	+	38.0159i	−0.323368	+	1.41677i
$721$	22.4894	+	10.8303i	0.837548	+	0.403342i
$722$	−39.4116	+	18.9796i	−1.46675	+	0.706348i
$723$	−5.81888	+	25.4942i	−0.216406	+	0.948138i
$724$	106.928			3.97396
$725$	−17.4993	−	18.1064i	−0.649908	−	0.672456i
$726$	−11.3294			−0.420472
$727$	6.13737	−	26.8896i	0.227622	−	0.997279i	−0.723950	−	0.689853i	$-0.757675\pi$
$727$	6.13737	−	26.8896i	0.227622	−	0.997279i	0.951572	−	0.307426i	$-0.0994677\pi$
$728$	42.1293	−	20.2884i	1.56142	−	0.751939i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	4.44152	−	19.4596i	0.164388	−	0.720231i
$731$	2.02900	+	8.88963i	0.0750453	+	0.328795i
$732$	−53.9165	+	25.9648i	−1.99281	+	0.959688i
$733$	−26.6783	+	33.4535i	−0.985384	+	1.23563i	−0.0135639	+	0.999908i	$0.504318\pi$
$733$	−26.6783	+	33.4535i	−0.985384	+	1.23563i	−0.971820	+	0.235724i	$0.924254\pi$
$734$	−49.7502	+	62.3848i	−1.83631	+	2.30267i
$735$	−3.87316	−	1.86521i	−0.142864	−	0.0687995i
$736$	12.1849	+	15.2794i	0.449142	+	0.563206i
$737$	−18.1517			−0.668627
$738$	12.8173	+	16.0724i	0.471812	+	0.591633i
$739$	−6.66662	−	29.2084i	−0.245236	−	1.07445i	−0.936175	−	0.351535i	$-0.885660\pi$
$739$	−6.66662	−	29.2084i	−0.245236	−	1.07445i	0.690939	−	0.722913i	$-0.257197\pi$
$740$	−24.7693	−	108.521i	−0.910538	−	3.98933i
$741$	2.35791	+	2.95673i	0.0866200	+	0.108618i
$742$	−32.8726			−1.20679
$743$	0.969337	+	1.21551i	0.0355615	+	0.0445928i	0.799294	−	0.600940i	$-0.205207\pi$
$743$	0.969337	+	1.21551i	0.0355615	+	0.0445928i	−0.763733	+	0.645533i	$0.776635\pi$
$744$	−44.5273	−	21.4432i	−1.63245	−	0.786147i
$745$	1.44233	−	1.80863i	0.0528429	−	0.0662630i
$746$	−32.2534	+	40.4445i	−1.18088	+	1.48078i
$747$	9.54570	−	4.59697i	0.349259	−	0.168194i
$748$	14.5146	+	63.5925i	0.530706	+	2.32517i
$749$	7.25389	−	31.7814i	0.265051	−	1.16127i
$750$	2.43486	+	1.17257i	0.0889084	+	0.0428160i
$751$	37.8839	−	18.2439i	1.38240	−	0.665731i	0.412894	−	0.910779i	$-0.364518\pi$
$751$	37.8839	−	18.2439i	1.38240	−	0.665731i	0.969511	+	0.245048i	$0.0788037\pi$
$752$	25.9464	−	113.679i	0.946169	−	4.14544i
$753$	−3.87652			−0.141268
$754$	−33.1785	+	3.16650i	−1.20829	+	0.115317i
$755$	−53.7765			−1.95713
$756$	−2.73605	+	11.9874i	−0.0995093	+	0.435979i
$757$	24.4696	−	11.7839i	0.889362	−	0.428294i	0.0673267	−	0.997731i	$-0.478553\pi$
$757$	24.4696	−	11.7839i	0.889362	−	0.428294i	0.822035	+	0.569437i	$0.192839\pi$
$758$	−20.7470	−	9.99124i	−0.753566	−	0.362898i
$759$	−0.685304	+	3.00251i	−0.0248750	+	0.108984i
$760$	9.69009	+	42.4551i	0.351497	+	1.54001i
$761$	31.5591	−	15.1980i	1.14402	−	0.550929i	0.236785	−	0.971562i	$-0.423906\pi$
$761$	31.5591	−	15.1980i	1.14402	−	0.550929i	0.907231	+	0.420633i	$0.138192\pi$
$762$	28.1841	−	35.3418i	1.02100	−	1.28030i
$763$	7.90970	−	9.91846i	0.286351	−	0.359072i
$764$	114.448	+	55.1151i	4.14057	+	1.99399i
$765$	−9.36957	−	11.7491i	−0.338757	−	0.424788i
$766$	75.8493			2.74055
$767$	7.05991	+	8.85285i	0.254919	+	0.319658i
$768$	2.46628	+	10.8055i	0.0889941	+	0.389909i
$769$	−4.80403	−	21.0478i	−0.173238	−	0.759004i	−0.984652	−	0.174532i	$-0.944159\pi$
$769$	−4.80403	−	21.0478i	−0.173238	−	0.759004i	0.811414	−	0.584472i	$-0.198698\pi$
$770$	32.0763	+	40.2224i	1.15595	+	1.44952i
$771$	1.61631			0.0582101
$772$	−51.2429	−	64.2566i	−1.84427	−	2.31264i
$773$	−39.9923	−	19.2593i	−1.43842	−	0.692709i	−0.457882	−	0.889013i	$-0.651392\pi$
$773$	−39.9923	−	19.2593i	−1.43842	−	0.692709i	−0.980543	+	0.196304i	$0.937106\pi$
$774$	−3.15491	+	3.95614i	−0.113401	+	0.142200i
$775$	16.8604	−	21.1422i	0.605642	−	0.759451i
$776$	129.297	−	62.2662i	4.64149	−	2.23523i
$777$	−3.63827	−	15.9403i	−0.130522	−	0.571856i
$778$	−16.2173	+	71.0528i	−0.581420	+	2.54737i
$779$	11.3175	+	5.45020i	0.405490	+	0.195274i
$780$	−33.5625	+	16.1629i	−1.20173	+	0.578724i
$781$	−2.16357	+	9.47923i	−0.0774187	+	0.339194i
$782$	−15.3257			−0.548045
$783$	2.94240	−	4.51024i	0.105153	−	0.161183i
$784$	−17.3243			−0.618724
$785$	0.276376	−	1.21088i	0.00986430	−	0.0432183i
$786$	−10.9979	+	5.29631i	−0.392282	+	0.188913i
$787$	−18.6719	−	8.99190i	−0.665580	−	0.320527i	0.0704104	−	0.997518i	$-0.477569\pi$
$787$	−18.6719	−	8.99190i	−0.665580	−	0.320527i	−0.735991	+	0.676991i	$0.763283\pi$
$788$	−14.7184	+	64.4856i	−0.524322	+	2.29720i
$789$	−5.04283	−	22.0941i	−0.179529	−	0.786569i
$790$	28.2466	−	13.6029i	1.00497	−	0.483968i
$791$	15.9573	−	20.0099i	0.567378	−	0.711469i
$792$	−13.8677	+	17.3896i	−0.492768	+	0.617911i
$793$	−23.9936	−	11.5547i	−0.852037	−	0.410319i
$794$	−8.28462	−	10.3886i	−0.294010	−	0.368677i
$795$	16.0916			0.570711
$796$	−26.2788	−	32.9525i	−0.931427	−	1.16797i
$797$	1.09838	+	4.81233i	0.0389068	+	0.170462i	0.990649	−	0.136438i	$-0.0435655\pi$
$797$	1.09838	+	4.81233i	0.0389068	+	0.170462i	−0.951742	+	0.306900i	$0.900708\pi$
$798$	2.31640	+	10.1488i	0.0819998	+	0.359265i
$799$	28.0178	+	35.1332i	0.991199	+	1.24292i
$800$	−77.2282			−2.73043
$801$	−3.55552	−	4.45848i	−0.125628	−	0.157533i
$802$	15.0230	+	7.23470i	0.530481	+	0.255466i
$803$	3.88401	−	4.87039i	0.137064	−	0.171872i
$804$	22.5570	−	28.2856i	0.795526	−	0.997558i
$805$	−7.86018	+	3.78526i	−0.277035	+	0.133413i
$806$	−7.96464	−	34.8954i	−0.280542	−	1.22914i
$807$	−1.16161	+	5.08934i	−0.0408906	+	0.179153i
$808$	35.2805	+	16.9902i	1.24116	+	0.597713i
$809$	−1.07371	+	0.517072i	−0.0377497	+	0.0181793i	−0.452663	−	0.891681i	$-0.649526\pi$
$809$	−1.07371	+	0.517072i	−0.0377497	+	0.0181793i	0.414914	+	0.909861i	$0.363812\pi$
$810$	1.85570	−	8.13036i	0.0652027	−	0.285672i
$811$	46.6639			1.63859			0.819296	−	0.573370i	$-0.194364\pi$
$811$	46.6639			1.63859			0.819296	+	0.573370i	$0.194364\pi$
$812$	−62.1168	−	22.9316i	−2.17987	−	0.804741i
$813$	−1.49938			−0.0525855
$814$	10.7108	−	46.9271i	0.375414	−	1.64480i
$815$	−27.7831	+	13.3796i	−0.973198	+	0.468668i
$816$	−54.5631	−	26.2762i	−1.91009	−	0.919852i
$817$	−0.688019	+	3.01441i	−0.0240707	+	0.105461i
$818$	2.76731	+	12.1244i	0.0967569	+	0.423920i
$819$	−4.92988	+	2.37411i	−0.172264	+	0.0829580i
$820$	−77.1464	+	96.7386i	−2.69407	+	3.37826i
$821$	19.7875	−	24.8127i	0.690588	−	0.865970i	−0.305694	−	0.952130i	$-0.598888\pi$
$821$	19.7875	−	24.8127i	0.690588	−	0.865970i	0.996281	+	0.0861603i	$0.0274597\pi$
$822$	53.1625	+	25.6017i	1.85425	+	0.892962i
$823$	−23.9132	−	29.9862i	−0.833561	−	1.04525i	−0.998263	−	0.0589096i	$-0.981238\pi$
$823$	−23.9132	−	29.9862i	−0.833561	−	1.04525i	0.164702	−	0.986343i	$-0.447334\pi$
$824$	−89.9964			−3.13517
$825$	−7.58797	−	9.51501i	−0.264179	−	0.331270i
$826$	6.93564	+	30.3870i	0.241322	+	1.05730i
$827$	3.81065	+	16.6955i	0.132509	+	0.580561i	0.996965	+	0.0778518i	$0.0248061\pi$
$827$	3.81065	+	16.6955i	0.132509	+	0.580561i	−0.864456	+	0.502709i	$0.832337\pi$
$828$	−3.82717	−	4.79912i	−0.133003	−	0.166781i
$829$	50.9294			1.76885			0.884425	−	0.466682i	$-0.154551\pi$
$829$	50.9294			1.76885			0.884425	+	0.466682i	$0.154551\pi$
$830$	55.0890	+	69.0794i	1.91217	+	2.39778i
$831$	1.96518	+	0.946380i	0.0681713	+	0.0328296i
$832$	−27.6466	+	34.6678i	−0.958474	+	1.20189i
$833$	4.16277	−	5.21994i	0.144231	−	0.180860i
$834$	19.5500	−	9.41477i	0.676960	−	0.326007i
$835$	8.11161	+	35.5393i	0.280714	+	1.22989i
$836$	−4.92179	+	21.5638i	−0.170224	+	0.745799i
$837$	5.21049	+	2.50924i	0.180101	+	0.0867320i
$838$	33.0144	−	15.8989i	1.14046	−	0.549218i
$839$	−8.56685	+	37.5338i	−0.295760	+	1.29581i	0.580613	+	0.814179i	$0.302813\pi$
$839$	−8.56685	+	37.5338i	−0.295760	+	1.29581i	−0.876374	+	0.481632i	$0.840044\pi$
$840$	−63.0066			−2.17393
$841$	22.0435	+	18.8437i	0.760121	+	0.649782i
$842$	31.9116			1.09974
$843$	−3.83346	+	16.7955i	−0.132031	+	0.578467i
$844$	98.1290	−	47.2564i	3.37774	−	1.62663i
$845$	21.4976	+	10.3527i	0.739540	+	0.356144i
$846$	−5.54910	+	24.3122i	−0.190782	+	0.835871i
$847$	−2.22883	−	9.76513i	−0.0765834	−	0.335534i
$848$	58.4264	−	28.1367i	2.00637	−	0.966217i
$849$	7.12677	−	8.93669i	0.244590	−	0.306707i
$850$	37.7600	−	47.3496i	1.29516	−	1.62408i
$851$	7.35409	+	3.54154i	0.252095	+	0.121403i
$852$	−12.0827	−	15.1513i	−0.413948	−	0.519074i
$853$	−19.5496			−0.669364			−0.334682	−	0.942331i	$-0.608629\pi$
$853$	−19.5496			−0.669364			−0.334682	+	0.942331i	$0.608629\pi$
$854$	−45.7046	−	57.3118i	−1.56398	−	1.96117i
$855$	−1.13391	−	4.96800i	−0.0387790	−	0.169902i
$856$	26.1534	+	114.586i	0.893905	+	3.91646i
$857$	−3.75869	−	4.71325i	−0.128394	−	0.161002i	0.713479	−	0.700677i	$-0.247118\pi$
$857$	−3.75869	−	4.71325i	−0.128394	−	0.161002i	−0.841873	+	0.539675i	$0.818547\pi$
$858$	−16.1084			−0.549933
$859$	9.53742	+	11.9596i	0.325413	+	0.408055i	0.917447	−	0.397858i	$-0.130246\pi$
$859$	9.53742	+	11.9596i	0.325413	+	0.408055i	−0.592034	+	0.805913i	$0.701675\pi$
$860$	−27.4401	−	13.2145i	−0.935701	−	0.450610i
$861$	−11.3318	+	14.2096i	−0.386185	+	0.484261i
$862$	37.9976	−	47.6475i	1.29420	−	1.62288i
$863$	4.59289	−	2.21182i	0.156344	−	0.0752913i	−0.354076	−	0.935217i	$-0.615204\pi$
$863$	4.59289	−	2.21182i	0.156344	−	0.0752913i	0.510419	+	0.859926i	$0.329490\pi$
$864$	−3.67518	−	16.1020i	−0.125032	−	0.547801i
$865$	−5.63667	+	24.6959i	−0.191653	+	0.839685i
$866$	−13.3107	−	6.41009i	−0.452315	−	0.217824i
$867$	5.71149	−	2.75051i	0.193972	−	0.0934122i
$868$	15.8232	−	69.3258i	0.537073	−	2.35307i
$869$	9.78469			0.331923
$870$	42.1301	+	15.5531i	1.42834	+	0.527300i
$871$	16.1000			0.545528
$872$	−10.1779	+	44.5924i	−0.344668	+	1.51009i
$873$	−15.1300	+	7.28624i	−0.512074	+	0.246602i
$874$	−4.68218	−	2.25482i	−0.158377	−	0.0762704i
$875$	−0.531661	+	2.32936i	−0.0179734	+	0.0787467i
$876$	2.76285	+	12.1048i	0.0933480	+	0.408984i
$877$	−50.7911	+	24.4597i	−1.71509	+	0.825945i	−0.724473	+	0.689303i	$0.757917\pi$
$877$	−50.7911	+	24.4597i	−1.71509	+	0.825945i	−0.990621	+	0.136642i	$0.956369\pi$
$878$	−33.8721	+	42.4742i	−1.14313	+	1.43344i
$879$	3.19509	−	4.00652i	0.107768	−	0.135137i
$880$	−91.4386	−	44.0345i	−3.08239	−	1.48440i
$881$	5.46459	+	6.85238i	0.184107	+	0.230863i	0.865317	−	0.501226i	$-0.167117\pi$
$881$	5.46459	+	6.85238i	0.184107	+	0.230863i	−0.681210	+	0.732088i	$0.738546\pi$
$882$	3.70510			0.124757
$883$	−27.7872	−	34.8440i	−0.935112	−	1.17259i	−0.984776	−	0.173828i	$-0.944386\pi$
$883$	−27.7872	−	34.8440i	−0.935112	−	1.17259i	0.0496640	−	0.998766i	$-0.484185\pi$
$884$	−12.8740	−	56.4046i	−0.432999	−	1.89709i
$885$	−3.39509	−	14.8749i	−0.114125	−	0.500013i
$886$	−56.6621	−	71.0520i	−1.90360	−	2.38704i
$887$	50.8916			1.70877			0.854386	−	0.519639i	$-0.173933\pi$
$887$	50.8916			1.70877			0.854386	+	0.519639i	$0.173933\pi$
$888$	36.7546	+	46.0888i	1.23340	+	1.54664i
$889$	36.0069	+	17.3400i	1.20763	+	0.581565i
$890$	29.6511	−	37.1812i	0.993905	−	1.24632i
$891$	1.62277	−	2.03489i	0.0543648	−	0.0681713i
$892$	−99.1180	+	47.7327i	−3.31872	+	1.59821i
$893$	3.39074	+	14.8558i	0.113467	+	0.497130i
$894$	−0.443660	+	1.94380i	−0.0148382	+	0.0650105i
$895$	−30.2076	−	14.5472i	−1.00973	−	0.486259i
$896$	−39.4281	+	18.9876i	−1.31720	+	0.634330i
$897$	0.607844	−	2.66314i	0.0202953	−	0.0889196i
$898$	−86.4734			−2.88566
$899$	−17.0165	+	26.0836i	−0.567533	+	0.869938i
$900$	24.2567			0.808556
$901$	−5.56119	+	24.3652i	−0.185270	+	0.811721i
$902$	−48.2064	+	23.2150i	−1.60510	+	0.772974i
$903$	−4.03058	−	1.94103i	−0.134129	−	0.0645933i
$904$	−20.5333	+	89.9624i	−0.682929	+	2.99211i
$905$	−14.2675	−	62.5100i	−0.474268	−	2.07790i
$906$	41.7586	−	20.1099i	1.38734	−	0.668106i
$907$	−13.8142	+	17.3225i	−0.458695	+	0.575185i	−0.956362	−	0.292183i	$-0.905618\pi$
$907$	−13.8142	+	17.3225i	−0.458695	+	0.575185i	0.497668	+	0.867368i	$0.334190\pi$
$908$	34.6218	−	43.4144i	1.14897	−	1.44076i
$909$	−4.12844	−	1.98815i	−0.136932	−	0.0659429i
$910$	−28.4507	−	35.6761i	−0.943132	−	1.18265i
$911$	2.98463			0.0988851			0.0494425	−	0.998777i	$-0.484256\pi$
$911$	2.98463			0.0988851			0.0494425	+	0.998777i	$0.484256\pi$
$912$	−12.8038	−	16.0554i	−0.423975	−	0.531648i
$913$	6.13615	+	26.8842i	0.203077	+	0.889738i
$914$	−15.5894	−	68.3016i	−0.515651	−	2.25921i
$915$	22.3731	+	28.0549i	0.739631	+	0.927468i
$916$	−72.6560			−2.40062
$917$	−6.72867	−	8.43748i	−0.222200	−	0.278630i
$918$	11.6693	+	5.61963i	0.385144	+	0.185475i
$919$	−2.67826	+	3.35843i	−0.0883475	+	0.110784i	−0.824041	−	0.566531i	$-0.808285\pi$
$919$	−2.67826	+	3.35843i	−0.0883475	+	0.110784i	0.735693	+	0.677315i	$0.236857\pi$
$920$	19.6115	−	24.5920i	0.646570	−	0.810774i
$921$	3.05458	−	1.47101i	0.100652	−	0.0484714i
$922$	−7.47869	−	32.7663i	−0.246298	−	1.07910i
$923$	1.91902	−	8.40779i	0.0631654	−	0.276746i
$924$	−28.8330	−	13.8853i	−0.948538	−	0.456792i
$925$	−29.0611	+	13.9951i	−0.955524	+	0.460156i
$926$	−22.7287	+	99.5808i	−0.746911	+	3.27243i
$927$	10.5312			0.345889
$928$	88.5396	−	8.45007i	2.90645	−	0.277387i
$929$	33.6586			1.10430			0.552152	−	0.833743i	$-0.313807\pi$
$929$	33.6586			1.10430			0.552152	+	0.833743i	$0.313807\pi$
$930$	−10.7319	+	47.0195i	−0.351913	+	1.54183i
$931$	2.03977	−	0.982301i	0.0668507	−	0.0321936i
$932$	57.8859	+	27.8764i	1.89612	+	0.913122i
$933$	3.80917	−	16.6891i	0.124707	−	0.546375i
$934$	−4.12181	−	18.0588i	−0.134870	−	0.590903i
$935$	35.2393	−	16.9704i	1.15245	−	0.554990i
$936$	12.3002	−	15.4240i	0.402046	−	0.504150i
$937$	15.0681	−	18.8947i	0.492252	−	0.617264i	−0.472210	−	0.881486i	$-0.656544\pi$
$937$	15.0681	−	18.8947i	0.492252	−	0.617264i	0.964462	+	0.264222i	$0.0851151\pi$
$938$	39.9283	+	19.2285i	1.30371	+	0.627832i
$939$	0.902925	+	1.13223i	0.0294658	+	0.0369490i
$940$	−150.096			−4.89561
$941$	−15.7291	−	19.7237i	−0.512755	−	0.642974i	0.456298	−	0.889827i	$-0.349175\pi$
$941$	−15.7291	−	19.7237i	−0.512755	−	0.642974i	−0.969053	+	0.246853i	$0.920604\pi$
$942$	0.238202	+	1.04363i	0.00776103	+	0.0340033i
$943$	−2.01899	−	8.84576i	−0.0657473	−	0.288058i
$944$	−38.3362	−	48.0721i	−1.24774	−	1.56461i
$945$	7.37288			0.239840
$946$	−8.21135	−	10.2967i	−0.266974	−	0.334775i
$947$	−43.3634	−	20.8827i	−1.40912	−	0.678597i	−0.434133	−	0.900849i	$-0.642945\pi$
$947$	−43.3634	−	20.8827i	−1.40912	−	0.678597i	−0.974989	+	0.222251i	$0.928659\pi$
$948$	−12.1594	+	15.2474i	−0.394919	+	0.495213i
$949$	−3.44500	+	4.31989i	−0.111829	+	0.140229i
$950$	18.5025	−	8.91035i	0.600302	−	0.289090i
$951$	−3.89788	−	17.0777i	−0.126398	−	0.553784i
$952$	21.7748	−	95.4015i	0.705725	−	3.09198i
$953$	−9.31899	−	4.48779i	−0.301872	−	0.145374i	0.276816	−	0.960923i	$-0.410721\pi$
$953$	−9.31899	−	4.48779i	−0.301872	−	0.145374i	−0.578688	+	0.815549i	$0.696435\pi$
$954$	−12.4955	+	6.01751i	−0.404557	+	0.194824i
$955$	16.9493	−	74.2597i	0.548466	−	2.40299i
$956$	46.1869			1.49379
$957$	9.74045	+	10.0784i	0.314864	+	0.325788i
$958$	40.8321			1.31922
$959$	−11.6082	+	50.8590i	−0.374850	+	1.64232i
$960$	53.8311	−	25.9237i	1.73739	−	0.836684i
$961$	−2.20329	−	1.06105i	−0.0710740	−	0.0342274i
$962$	−9.50016	+	41.6229i	−0.306298	+	1.34198i
$963$	−3.06041	−	13.4085i	−0.0986204	−	0.432084i
$964$	122.220	−	58.8579i	3.93643	−	1.89568i
$965$	−30.7268	+	38.5302i	−0.989131	+	1.24033i
$966$	4.68809	−	5.87868i	0.150837	−	0.189143i
$967$	17.7741	+	8.55958i	0.571578	+	0.275257i	0.697266	−	0.716812i	$-0.254400\pi$
$967$	17.7741	+	8.55958i	0.571578	+	0.275257i	−0.125688	+	0.992070i	$0.540114\pi$
$968$	22.5161	+	28.2342i	0.723693	+	0.907483i
$969$	7.91418			0.254240
$970$	−87.3166	−	109.492i	−2.80357	−	3.51556i
$971$	1.86443	+	8.16861i	0.0598325	+	0.262143i	0.995993	−	0.0894292i	$-0.0285043\pi$
$971$	1.86443	+	8.16861i	0.0598325	+	0.262143i	−0.936161	+	0.351572i	$0.885647\pi$
$972$	1.15434	+	5.05749i	0.0370255	+	0.162219i
$973$	11.9610	+	14.9986i	0.383451	+	0.480832i
$974$	84.8821			2.71980
$975$	6.73029	+	8.43952i	0.215542	+	0.270281i
$976$	130.288	+	62.7435i	4.17042	+	2.00837i
$977$	17.2562	−	21.6385i	0.552073	−	0.692278i	−0.424997	−	0.905195i	$-0.639725\pi$
$977$	17.2562	−	21.6385i	0.552073	−	0.692278i	0.977070	+	0.212917i	$0.0682963\pi$
$978$	16.5708	−	20.7791i	0.529876	−	0.664444i
$979$	13.3724	−	6.43983i	0.427385	−	0.205818i
$980$	4.96237	+	21.7416i	0.158517	+	0.694509i
$981$	1.19100	−	5.21810i	0.0380256	−	0.166601i
$982$	25.9125	+	12.4788i	0.826901	+	0.398214i
$983$	1.62240	−	0.781309i	0.0517466	−	0.0249199i	−0.407831	−	0.913057i	$-0.633715\pi$
$983$	1.62240	−	0.781309i	0.0517466	−	0.0249199i	0.459578	+	0.888137i	$0.348001\pi$
$984$	14.5813	−	63.8849i	0.464835	−	2.03658i
$985$	39.6619			1.26373
$986$	−38.1098	+	58.4163i	−1.21366	+	1.86035i
$987$	−22.0471			−0.701768
$988$	4.36548	−	19.1264i	0.138884	−	0.608492i
$989$	2.01216	−	0.969005i	0.0639830	−	0.0308126i
$990$	19.5557	+	9.41755i	0.621522	+	0.299309i
$991$	−3.73734	+	16.3743i	−0.118720	+	0.520148i	0.880239	+	0.474531i	$0.157382\pi$
$991$	−3.73734	+	16.3743i	−0.118720	+	0.520148i	−0.998959	+	0.0456167i	$0.985475\pi$
$992$	21.2543	+	93.1212i	0.674825	+	2.95660i
$993$	9.39498	−	4.52438i	0.298141	−	0.143577i
$994$	14.8008	−	18.5596i	0.469452	−	0.588674i
$995$	−15.7576	+	19.7594i	−0.499548	+	0.626414i
$996$	−49.5188	−	23.8470i	−1.56906	−	0.755622i
$997$	16.6174	+	20.8376i	0.526280	+	0.659934i	0.971929	−	0.235274i	$-0.0755987\pi$
$997$	16.6174	+	20.8376i	0.526280	+	0.659934i	−0.445650	+	0.895208i	$0.647027\pi$
$998$	26.1921			0.829096
$999$	−4.30094	−	5.39321i	−0.136076	−	0.170633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.b.25.3	yes	18
3.2	odd	2		261.2.k.b.199.1		18
29.6	even	14		2523.2.a.q.1.9		9
29.7	even	7	inner	87.2.g.b.7.3	✓	18
29.23	even	7		2523.2.a.p.1.1		9
87.23	odd	14		7569.2.a.bl.1.9		9
87.35	odd	14		7569.2.a.bk.1.1		9
87.65	odd	14		261.2.k.b.181.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.7.3	✓	18	29.7	even	7	inner
87.2.g.b.25.3	yes	18	1.1	even	1	trivial
261.2.k.b.181.1		18	87.65	odd	14
261.2.k.b.199.1		18	3.2	odd	2
2523.2.a.p.1.1		9	29.23	even	7
2523.2.a.q.1.9		9	29.6	even	14
7569.2.a.bk.1.1		9	87.35	odd	14
7569.2.a.bl.1.9		9	87.23	odd	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.596570 - 2.61374i) q^{2} +(0.900969 - 0.433884i) q^{3} +(-4.67383 - 2.25080i) q^{4} +(-0.692177 + 3.03263i) q^{5} +(-0.596570 - 2.61374i) q^{6} +(2.13550 - 1.02840i) q^{7} +(-5.32817 + 6.68131i) q^{8} +(0.623490 - 0.781831i) q^{9} +(7.51358 + 3.61835i) q^{10} +(1.62277 + 2.03489i) q^{11} -5.18756 q^{12} +(-1.43935 - 1.80488i) q^{13} +(-1.41401 - 6.19518i) q^{14} +(0.692177 + 3.03263i) q^{15} +(7.81583 + 9.80074i) q^{16} -4.83107 q^{17} +(-1.67155 - 2.09606i) q^{18} +(-1.47595 - 0.710781i) q^{19} +(10.0609 - 12.6160i) q^{20} +(1.47782 - 1.85312i) q^{21} +(6.28677 - 3.02755i) q^{22} +(0.263303 + 1.15361i) q^{23} +(-1.90160 + 8.33146i) q^{24} +(-4.21288 - 2.02881i) q^{25} +(-5.57617 + 2.68534i) q^{26} +(0.222521 - 0.974928i) q^{27} -12.2957 q^{28} +(5.05191 + 1.86501i) q^{29} +8.33945 q^{30} +(-1.28688 + 5.63821i) q^{31} +(14.8805 - 7.16606i) q^{32} +(2.34497 + 1.12928i) q^{33} +(-2.88207 + 12.6272i) q^{34} +(1.64062 + 7.18803i) q^{35} +(-4.67383 + 2.25080i) q^{36} +(4.30094 - 5.39321i) q^{37} +(-2.73831 + 3.43373i) q^{38} +(-2.07992 - 1.00163i) q^{39} +(-16.5739 - 20.7830i) q^{40} -7.66791 q^{41} +(-3.96197 - 4.96815i) q^{42} +(-0.419989 - 1.84009i) q^{43} +(-3.00442 - 13.1632i) q^{44} +(1.93944 + 2.43198i) q^{45} +3.17231 q^{46} +(-5.79950 - 7.27234i) q^{47} +(11.2942 + 5.43900i) q^{48} +(-0.861665 + 1.08049i) q^{49} +(-7.81608 + 9.80105i) q^{50} +(-4.35265 + 2.09612i) q^{51} +(2.66483 + 11.6754i) q^{52} +(1.15113 - 5.04343i) q^{53} +(-2.41546 - 1.16323i) q^{54} +(-7.29430 + 3.51275i) q^{55} +(-4.50723 + 19.7475i) q^{56} -1.63818 q^{57} +(7.88847 - 12.0918i) q^{58} -4.90494 q^{59} +(3.59071 - 15.7319i) q^{60} +(10.3934 - 5.00522i) q^{61} +(13.9691 + 6.72717i) q^{62} +(0.527426 - 2.31080i) q^{63} +(-4.27413 - 18.7262i) q^{64} +(6.46982 - 3.11570i) q^{65} +(4.35058 - 5.45546i) q^{66} +(-4.34830 + 5.45260i) q^{67} +(22.5796 + 10.8738i) q^{68} +(0.737759 + 0.925121i) q^{69} +19.7664 q^{70} +(2.32918 + 2.92070i) q^{71} +(1.90160 + 8.33146i) q^{72} +(-0.532592 - 2.33344i) q^{73} +(-11.5306 - 14.4590i) q^{74} -4.67594 q^{75} +(5.29852 + 6.64413i) q^{76} +(5.55812 + 2.67665i) q^{77} +(-3.85883 + 4.83882i) q^{78} +(2.34395 - 2.93923i) q^{79} +(-35.1319 + 16.9187i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-4.57445 + 20.0420i) q^{82} +(9.54570 + 4.59697i) q^{83} +(-11.0780 + 5.33491i) q^{84} +(3.34396 - 14.6508i) q^{85} -5.06009 q^{86} +(5.36081 - 0.511626i) q^{87} -22.2421 q^{88} +(1.26895 - 5.55963i) q^{89} +(7.51358 - 3.61835i) q^{90} +(-4.92988 - 2.37411i) q^{91} +(1.36590 - 5.98440i) q^{92} +(1.28688 + 5.63821i) q^{93} +(-22.4678 + 10.8199i) q^{94} +(3.17715 - 3.98402i) q^{95} +(10.2976 - 12.9128i) q^{96} +(-15.1300 - 7.28624i) q^{97} +(2.31009 + 2.89676i) q^{98} +2.60272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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